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KhatamKahani

@KhatamKahani

Stunner

Posted: 13 years ago

#31

42 (forty-two) is the natural number immediately following 41 and directly preceding 43. The number has received considerable attention in popular culture as a result of its central appearance in The Hitchhiker's Guide to the Galaxy as the "Answer to the Ultimate Question of Life, the Universe, and Everything".

Given 27 same-size cubes whose nominal values progress from 1 to 27, a 333 magic cube can be constructed such that every row, column, and corridor, and every diagonal passing through the center, is composed of 3 cubes whose sum of values is 42.
Forty-two is a pronic number and an abundant number; its prime factorization 2 3 7 makes it the second sphenic number and also the second of the form { 2 3 r }. As with all sphenic numbers of this form, the aliquot sum is abundant by 12. 42 is also the second sphenic number to be bracketed bytwin primes; 30 is also a pronic number and also rests between two primes. 42 has a 14 member aliquot sequence 42, 54, 66, 78, 90, 144, 259, 45, 33, 15, 9, 4, 3, 1, 0 and is itself part of the aliquot sequence commencing with the first sphenic number 30. Further, 42 is the 10th member of the 3-aliquot tree.
42 is the product of the first three terms of Sylvester's sequence; like the first five such numbers it is also a primary pseudoperfect number.
It is a Catalan number. Consequently; 42 is the number of noncrossing partitions of a set of five elements, the number of triangulations of a heptagon, the number of rooted ordered binary trees with six leaves, the number of ways in which five pairs of nested parentheses can be arranged, etc.
It is the reciprocal of the sixth Bernoulli number.
It is conjectured to be the scaling factor in the leading order term of the "sixth moment of the Riemann zeta function". In particular, Conrey & Ghosh have conjectured
${1 \over T}\int_0^T \left| \zeta\left({1 \over 2} + it\right) \right|^6\,dt \sim {42 \over 9!}\prod_p \left\{1-{1\over p}\right\}^4 \left( 1 + {4 \over p} + {1 \over p^2} \right) \log^9 T,$
where the infinite product is over all prime numbers, p.^[1]^[2]
It is the third pentadecagonal number. It is a meandric number and an open meandric number.
42 is a Strmer number.

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-Nakshatra-

@-Nakshatra-

Dazzler

+ 2

Posted: 13 years ago

#32

43

43 is the smallest prime that is not a Chen prime. It is also the third Wagstaff prime.

43 is the fourth term of Sylvester's sequence, one more than the product of the previous terms (2 3 7).

Sheils where are you 😆 😆

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KhatamKahani

@KhatamKahani

Stunner

Posted: 13 years ago

#33

We scared her away. 🤣

Forty-four is a tribonacci number, a happy number, an octahedral number and a palindromic number.

Since the greatest prime factor of 44² + 1 = 1937 is 149 and thus more than 44 twice, 44 is a Strmer number.

The aliquot sequence of 44 is (44,40,50,43,1,0).

Given Euler's totient function, $\varphi(44)=20$ and $\varphi(69)=44.$

44 is the number of derangements of 5 items.

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Rani

@pyar-ishk

Trailblazer

+ 7

Posted: 13 years ago

#34

You guys have 45 screw loose 🤣 🤣 🤣

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-Nakshatra-

@-Nakshatra-

Dazzler

+ 2

Posted: 13 years ago

#35

Sahiba you are 46th Nut on the row 🤣 🤣

Forty-six is a Wedderburn-Etherington number, an enneagonal number and a centered triangular number. It is the sum of the totient function for the first twelve integers. 46 is the largest even integer that can't be expressed as a sum of two abundant numbers.

46 is the 13th semiprime. 46 is the third semiprime with a semiprime aliquot sum. The aliquot sequence of 46 is (46,26,16,15,9,4,3,1,0).

Since it is possible to find sequences of 46 consecutive integers such that each inner member shares a factor with either the first or the last member, 46 is an Erdos'Woods number.

Edited by -Nakshatra- - 13 years ago

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KhatamKahani

@KhatamKahani

Stunner

Posted: 13 years ago

#36

A screw, or bolt, is a type of fastener characterized by a helical ridge, known as an external thread or just thread, wrapped around a cylinder. Some screw threads are designed to mate with a complementary thread, known as an internal thread, often in the form of a nut or an object that has the internal thread formed into it. Other screw threads are designed to cut a helical groove in a softer material as the screw is inserted. The most common uses of screws are to hold objects together and to position objects.

Often screws have a head, which is a specially formed section on one end of the screw that allows it to be turned, or driven. Common tools for driving screws include screwdrivers and wrenches. The head is usually larger than the body of the screw, which keeps the screw from being driven deeper than the length of the screw and to provide a bearing surface. There are exceptions; for instance, carriage bolts have a domed head that is not designed to be driven; set screws have a head smaller than the outer diameter of the screw; J-bolts have a J-shaped head which is not designed to be driven, but rather is usually sunk into concrete allowing it to be used as an anchor bolt. The cylindrical portion of the screw from the underside of the head to the tip is known as the shank; it may be fully threaded or partially threaded.^[1] The distance between each thread is called the "pitch".

The majority of screws are tightened by clockwise rotation, which is termed a right-hand thread; a common mnemonic device for remembering this when working with screws or bolts is "lefty-loosy, righty-tighty." Screws with left-hand threads are used in exceptional cases. For example, when the screw will be subject to counterclockwise torque (which would work to undo a right-hand thread), a left-hand-threaded screw would be an appropriate choice. The left side pedal of a bicycle has a left-hand thread.

More generally, screw may mean any helical device, such as a clamp, a micrometer, a ship's propeller or an Archimedes' screw water pump

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KhatamKahani

@KhatamKahani

Stunner

Posted: 13 years ago

#37

Forty-seven is the fifteenth prime number, a safe prime, the thirteenth supersingular prime, and the sixth Lucas prime. Forty-seven is a highly cototient number. It is an Eisenstein prime with no imaginary part and real part of the form $3n - 1$ .

It is a Lucas number. Because its digits appear as successive terms earler in the series of Lucas numbers: 2, 1, 3, 4, 7, 11, 18, 29, 47… ; it is also a Keith number.

Forty-seven is a strictly non-palindromic number.

Its representation in binary being 00101111, 47 is a prime Thabit number, and as such is related to the pair of amicable numbers {17296, 18416}.

Forty-seven is a Carol number. It is a real prime number.

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-Nakshatra-

@-Nakshatra-

Dazzler

+ 2

Posted: 13 years ago

#38

Forty-eight is a double factorial of 6, a highly composite number. Like all other multiples of 6, it is a semiperfect number. 48 is the second 17-gonal number.

48 is in abundance having an aliquot sum of 76. It is the lowest composite number to fall into the 41-aliquot tree having the 7 aliquot number sequence,(48, 76 , 64, 63, 41, 1, 0). 48 is highly abundant with an aliquot sum 158% higher than itself.

48 is the smallest number with exactly ten divisors.

There are 11 solutions to the equation f(x) = 48, namely 65, 104, 105, 112, 130, 140, 144, 156, 168, 180 and 210. This is more than any integer below 48, making 48 a highly totient number.

Since the greatest prime factor of 48² + 1 = 2305 is 461, which is clearly more than 48 twice, 48 is a Strmer number.

48 is in base 10 a Harshad number. It has 24, 2, 12,and 4 as factors.

Edited by -Nakshatra- - 13 years ago