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%I #9 Dec 08 2022 07:29:51
%S 1,10,45,50,130,250,315,410,735,1125,1250,1690,2050,2205,2210,2373,
%T 2565,2745,3045,3250,3285,3321,3465,3645,4225,5050,5330,6125,6250,
%U 6615,6890,7875,8619,8835,9135,9225,9555,9933,10250
%N Numbers n dividing the sum of n-th powers of unitary divisors of n.
%H Robert Israel, <a href="/A238982/b238982.txt">Table of n, a(n) for n = 1..1000</a>
%p udivs:= proc(n) local t,F;
%p F:= map(t -> t[1]^t[2], ifactors(n)[2]);
%p map(convert, combinat:-powerset(F),`*`);
%p end proc:
%p filter:= proc(n) local t,U;
%p convert(map(t -> (t &^ n) mod n, udivs(n)),`+`) mod n = 0
%p end proc:
%p select(filter, [$1..20000]); # _Robert Israel_, Dec 07 2022
%t AA[n_, k_] := AA[n, k] = Mod[Sum[If[GCD[i, n] == i && GCD[i, n/i] == 1, PowerMod[i, k, n], 0], {i, n}], n]; Select[Range[1000], Mod[AA[#, #], #] == 0 &]
%Y Cf. A034448, A238981, A238983.
%K nonn
%O 1,2
%A _José María Grau Ribas_, Mar 07 2014
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