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

1,2

Links

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

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 &]

Crossrefs

Cf. A034448, A238981, A238983.

Sequence in context: A160970 A202296 A299530 * A292611 A275623 A245871

Adjacent sequences: A238979 A238980 A238981 * A238983 A238984 A238985

Keyword

nonn

Author

José María Grau Ribas, Mar 07 2014

Status

approved