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

%I A323251 #30 Feb 14 2019 16:08:14
%S A323251 22,80,625,1664,2392,4030,5434,5830,6118,6536,9614,11438,12958,13184,
%T A323251 15064,15314,17528,18632,18970,22570,23254,25234,29810,32128,33784,
%U A323251 34846,36938,37910,40610,43054,46664,52936,53354,58102,58646,60298,79378,79864,83266,92302,93056
%N A323251 Sequence lists numbers k > 1 such that k^4 == d(k) (mod sigma(k)), where d = A000005 and sigma = A000203.
%H A323251 Jinyuan Wang, <a href="/A323251/b323251.txt">Table of n, a(n) for n = 1..1000</a>
%F A323251 Solutions of k^4 mod sigma(k) = d(k).
%e A323251 sigma(22) = 36 and 22^4 mod 36 = 4 = d(22).
%p A323251 with(numtheory): op(select(n->n^4 mod sigma(n)=tau(n),[$1..92302]));
%t A323251 Select[Range[10^5], PowerMod[#1, 4, #3] == #2 & @@ Prepend[DivisorSigma[{0, 1}, #], #] &] (* _Michael De Vlieger_, Jan 18 2019 *)
%o A323251 (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 A323251 Cf. A000005, A000203, A323249, A323250.
%K A323251 nonn,easy
%O A323251 1,1
%A A323251 _Paolo P. Lava_, Jan 08 2019