A323251 Sequence lists numbers k > 1 such that k^4 == d(k) (mod sigma(k)), where d = A000005 and sigma = A000203.

22, 80, 625, 1664, 2392, 4030, 5434, 5830, 6118, 6536, 9614, 11438, 12958, 13184, 15064, 15314, 17528, 18632, 18970, 22570, 23254, 25234, 29810, 32128, 33784, 34846, 36938, 37910, 40610, 43054, 46664, 52936, 53354, 58102, 58646, 60298, 79378, 79864, 83266, 92302, 93056

Offset: 1

Author

Paolo P. Lava, Jan 08 2019

Keywords

• nonn
• easy

Examples

			sigma(22) = 36 and 22^4 mod 36 = 4 = d(22).
		

Links

• Jinyuan Wang, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000005, A000203, A323249, A323250.

Programs

Maple

with(numtheory): op(select(n->n^4 mod sigma(n)=tau(n),[$1..92302]));

Mathematica

Select[Range[10^5], PowerMod[#1, 4, #3] == #2 & @@ Prepend[DivisorSigma[{0, 1}, #], #] &] (* Michael De Vlieger, Jan 18 2019 *)

PARI

for(k=1, 10^5, x=sigma(k); if(Mod(k, x)^4==Mod(numdiv(k), x), print1(k, ", "))) \\ Jinyuan Wang, Feb 03 2019

Formula

Solutions of k^4 mod sigma(k) = d(k).