GOTW- Counting - Page 15

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Marvel-freak

@Marvel-freak

Dazzler

+ 2

Posted: 13 years ago

#141

One hundred [and] fourteen is an abundant number, a sphenic number and a Harshad number. It is the sum of the first four hyperfactorials, including H(0). At 114, the Mertens function sets a new low of -6, a record that stands until 197.

There is no answer to the equation f(x) = 114, making 114 a nontotient.

114 appears in the Padovan sequence, preceded by the terms 49, 65, 86 (it is the sum of the first two of these).

114 is a repdigit in base 7 (222). 😆😆😆

Edited by sheila1990 - 13 years ago

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KhatamKahani

@KhatamKahani

Stunner

Posted: 13 years ago

#142

Originally posted by: -Nakshatra-
You edited after i posted 😡

Doesn't matter. She gets first dibs, cause it's the duty of the person who repeats the number to edit to the next number. So by default it was her number anyway. The only reason this is being discussed is cause it's a Harshad number. 😆

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-Nakshatra-

@-Nakshatra-

Dazzler

+ 2

Posted: 13 years ago

#143

115 is a heptagonal pyramidal number and a lucky number. Because 115 has an odd number of 1s in its binary representation, it is sometimes called an "odious number."

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KhatamKahani

@KhatamKahani

Stunner

Posted: 13 years ago

#144

Chitra, you know 112 was a Harshad number, right?

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KhatamKahani

@KhatamKahani

Stunner

Posted: 13 years ago

#145

116 is a noncototient, meaning that there is no solution to the equation m - f(m) = n, where f stands for Euler's totient function.^[1] 116! + 1 is prime.^[2]There are 116 ternary Lyndon words of length six, and 116 irreducible polynomials of degree six over a three-element field, which form the basis of a free Lie algebra of dimension 116.^[3] There are 116 different ways of partitioning the numbers from 1 through 5 into subsets in such a way that, for every k, the union of the first k subsets is a consecutive sequence of integers.^[4] There are 116 different 66 Costas arrays.^[5]

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-Nakshatra-

@-Nakshatra-

Dazzler

+ 2

Posted: 13 years ago

#146

One hundred seventeen is the smallest possible length of the longest side of a Heronian tetrahedron (one whose sides are all rational numbers).^[1]^[2]

117 is a pentagonal number.

In base 10, it is a Harshad number.

Yes I do 😆

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Marvel-freak

@Marvel-freak

Dazzler

+ 2

Posted: 13 years ago

#147

Originally posted by: likarsh

Doesn't matter. She gets first dibs, cause it's the duty of the person who repeats the number to edit to the next number. So by default it was her number anyway. The only reason this is being discussed is cause it's a Harshad number. 😆

😆😆😆

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-Nakshatra-

@-Nakshatra-

Dazzler

+ 2

Posted: 13 years ago

#148

You can't call me cheater anymore 😡

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KhatamKahani

@KhatamKahani

Stunner

Posted: 13 years ago

#149

There is no answer to the equation f(x) = 118, making 118 a nontotient.

118 is the smallest n such that the range n, n + 1, ... 4n/3 contains at least one prime from each of these forms: 4x + 1, 4x - 1, 6x + 1 and 6x - 1.

Another way in which 118 is the smallest is that there are no smaller integers that can be expressed as the sum of three integers such that each set of three has the same product. For 118, those are 14 + 50 + 54 = 15 + 40 + 63 = 18 + 30 + 70 = 21 + 25 + 72.^[1]