A238982 Numbers n dividing the sum of n-th powers of unitary divisors of n.

1, 10, 45, 50, 130, 250, 315, 410, 735, 1125, 1250, 1690, 2050, 2205, 2210, 2373, 2565, 2745, 3045, 3250, 3285, 3321, 3465, 3645, 4225, 5050, 5330, 6125, 6250, 6615, 6890, 7875, 8619, 8835, 9135, 9225, 9555, 9933, 10250

Offset: 1

Author

José María Grau Ribas, Mar 07 2014

Keywords

• nonn

Links

• Robert Israel, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A034448, A238981, A238983.

Programs

Maple

udivs:= proc(n) local t,F;
  F:= map(t -> t[1]^t[2], ifactors(n)[2]);
  map(convert, combinat:-powerset(F),`*`);
end proc:
filter:= proc(n) local t,U;
  convert(map(t -> (t &^ n) mod n, udivs(n)),`+`) mod n = 0
end proc:
select(filter, [$1..20000]); # Robert Israel, Dec 07 2022

Mathematica

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 &]