A130073 Numbers k such that k divides 5^k - 3^k - 2^k = A130072(k).

1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 15, 16, 17, 18, 19, 23, 24, 25, 27, 29, 31, 32, 36, 37, 41, 43, 44, 45, 47, 48, 53, 54, 59, 61, 64, 67, 71, 72, 73, 75, 79, 81, 83, 89, 95, 96, 97, 101, 103, 107, 108, 109, 113, 125, 127, 128, 131, 133, 135, 137, 139, 144, 149, 151

Offset: 1

Author

Alexander Adamchuk, May 06 2007

Keywords

• nonn

Comments

All primes are the terms of a(n). Quotients A130072(p)/p for p = Prime(n) are listed in A130075(n) = {6,30,570,10830,4422630,93776970,44871187170,1003806502230,...}. p^(k+1) divides A130072(p^k) for prime p = {2,3,5,19} = A130076(n) and all k>0. Nonprimes n such that n divides A130072(n) are listed in A130074(n) = {1,4,6,8,9,12,15,16,18,24,25,27,32,36,44,45,48,54,64,72,75,81,95,96,...} which apparently include all powers p^k of primes p = {2,3,5,19} for k>1 and all powers of numbers of the form 2^k*3^m, 3^k*5^m, 5^k*19^m.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A130072, A130074, A130075, A130076.

Programs

Mathematica

Select[Range[1000],IntegerQ[(PowerMod[5,#,# ]-PowerMod[3,#,# ]-PowerMod[2,#,# ])/# ]&]

PARI

is(n)=Mod(5,n)^n==Mod(3,n)^n+Mod(2,n)^n \\ Charles R Greathouse IV, Nov 04 2016