GOTW- Counting - Page 10

Seventy-seven is the 22nd discrete biprime and the first of the (7.q) family. Since both 7 and 11 are Gaussian primes, this means that 77 is a Blum integer.

It is the sum of three squares, 4² + 5² + 6², as well as the sum of the first eight prime numbers.

77 has a aliquot sum of 19 and it is the second number to do so the first being 65. 77 is the 2nd member of the 19-aliquot tree.

77 and 78 form a Ruth–Aaron pair under the second definition in which repeated prime factors are counted as often as they occur.

It is possible for a sudoku puzzle to have as many as 77 givens, yet lack a unique solution.^[1]

It and its sibling 49 are the only 2-digit numbers whose home primes have not been calculated.

It is the number of digits of the 12th perfect number.^[2] It also is the number of integer partitions of the number 12.^[3]

Originally posted by: pyar-ishk

Thanks for enforcing the rules Lik 🤣

76

78 is a triangular number, and its factorization makes it a sphenic number. As a multiple of a perfect number, 78 is itself a semiperfect number.

77 and 78 form a Ruth-Aaron pair under the second definition in which repeated prime factors are counted as often as they occur.

Since it is possible to find sequences of 78 consecutive integers such that each inner member shares a factor with either the first or the last member, 78 is an Erdos–Woods number.

Karl A. Dahlke proved in 1989 that 78 heptominos of this shape ( ), at a minimum, are required to fill a rectangle

Seventy-nine is the natural number following 78 and preceding 80.^{[citation needed]}

79 may represent:

An odd number[edit]In mathematics

• The smallest number that can't be represented as a sum of fewer than 19 fourth powers
• A strictly non-palindromic number
• The 22nd prime number (the next is 83)
• The smallest prime number p for which the real quadratic field Q[vp] has class number greater than 1 (namely 3)^[1]
• A cousin prime with 83
• An emirp, because the reverse of 79, 97, is also a prime
• A fortunate prime
• A prime number that is also a Gaussian prime (since it is of the form )
• A happy prime
• A Higgs prime
• A Kynea prime ()
• A lucky prime
• A permutable prime, with ninety-seven
• A Pillai prime, because 23! + 1 is divisible by 79, but 79 is not one more than a multiple of 23
• A regular prime
• A prime in a residue classes 4n+3, 8n+7, and 10n+9
• A right-truncatable prime, because when the last digit (9) is removed, the remaining number (7) is still prime
• A sexy prime (with 73)
• The n value of the Wagstaff prime 201487636602438195784363

The sum of Euler's totient function f(x) over the first sixteen integers is 80.

Adding up some subsets of its divisors (e.g., 1, 4, 5, 10, 20 and 40) gives 80, hence 80 is a semiperfect number.

80 is a mnage number, and is a Harshad number number in base 10.

The Pareto principle (also known as the "80-20 rule," states that, for many events, roughly 80% of the effects come from 20% of the causes.^[1][2]