A130074 Nonprimes k such that k divides 5^k - 3^k - 2^k = A130072(k).

1, 4, 6, 8, 9, 12, 15, 16, 18, 24, 25, 27, 32, 36, 44, 45, 48, 54, 64, 72, 75, 81, 95, 96, 108, 125, 128, 133, 135, 144, 162, 175, 192, 216, 225, 243, 256, 264, 288, 324, 325, 361, 375, 384, 405, 432, 475, 486, 512, 561, 576, 594, 618, 625, 648, 675, 704, 729, 768

Offset: 1

Author

Alexander Adamchuk, May 06 2007

Keywords

• nonn

Comments

Numbers k such that k divides A130072(k) are listed in A130073(n) = {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,...}, which includes all primes. a(n) includes nonprimes in A130073(n). p^(k+1) divides A130072(p^k) for prime p = {2,3,5,19} = A130076(n) and all k>0. It appears that a(n) includes 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, A130073, A130075, A130076.

Programs

Mathematica

Select[Range[10000],!PrimeQ[ # ]&&IntegerQ[(PowerMod[5,#,# ]-PowerMod[3,#,# ]-PowerMod[2,#,# ])/# ]&]