Sunday, January 21, 2018

Number of the day: 7775

Properties of the number 7775:

7775 = 52 × 311 is the 6789th composite number and is not squarefree.
7775 has 2 distinct prime factors, 6 divisors, 11 antidivisors and 6200 totatives.
7775 has an emirpimes digit sum 26 in base 10.
Reversing the decimal digits of 7775 results in a semiprime.
7775 = 65 - 15 is the difference of 2 positive fifth powers in 1 way.
7775 = 38882 - 38872 = 7802 - 7752 = 1682 - 1432 is the difference of 2 nonnegative squares in 3 ways.
7775 is the difference of 2 positive pentagonal numbers in 3 ways.
7775 is not the sum of 3 positive squares.
77752 = 46652 + 62202 = 21772 + 74642 is the sum of 2 positive squares in 2 ways.
77752 is the sum of 3 positive squares.
7775 is a proper divisor of 88110 - 1.
7775 is palindromic in (at least) the following bases: 6, 37, -42, and -58.
7775 in base 6 = 55555 and consists of only the digit '5'.
7775 consists of only the digits '5' and '7'.
7775 in base 36 = 5zz and consists of only the digits '5' and 'z'.
7775 in base 37 = 5P5 and consists of only the digits '5' and 'P'.

The number 7775 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A014946: Numbers n such that n divides 6^n-1.
A024062: a(n) = 6^n-1.
A037205: a(n) = (n+1)^n - 1.
A079907: Numbers n such that 11*12^n -1 is prime.
A104621: Heptanacci-Lucas numbers.
A116632: Positive integers n such that 13^n == 7 (mod n).
A140811: 6n^2 - 1.
A141530: 4*n^3-6*n^2+1
A181288: Numbers of the form i*6^j-1 (i=1..5, j >= 0).
A292737: Numbers in which 7 outnumbers all other digits together.

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