A323251 - OEIS

A323251

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

%I #30 Feb 14 2019 16:08:14

%S 22,80,625,1664,2392,4030,5434,5830,6118,6536,9614,11438,12958,13184,

%T 15064,15314,17528,18632,18970,22570,23254,25234,29810,32128,33784,

%U 34846,36938,37910,40610,43054,46664,52936,53354,58102,58646,60298,79378,79864,83266,92302,93056

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

%H Jinyuan Wang, <a href="/A323251/b323251.txt">Table of n, a(n) for n = 1..1000</a>

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

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

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

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

%o (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

%Y Cf. A000005, A000203, A323249, A323250.

%K nonn,easy

%O 1,1

%A _Paolo P. Lava_, Jan 08 2019