A238981 -id:A238981 - cp's OEIS frontend

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

José María Grau Ribas, Mar 07 2014

nonn

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

Cf. A034448, A238981, A238983.

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

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 &]

A238983 Numbers n such that the sum of n-th powers of unitary divisors of n is congruent to -1 modulo n.

Original entry on oeis.org

1, 2, 265, 49217, 7870171, 592258417

Offset: 1

José María Grau Ribas, Mar 07 2014

a(7) > 10^10. - Hiroaki Yamanouchi, Oct 02 2014

Cf. A034448, A238981, A238982.

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[#, #], #] == #-1 &]

isok(n) = (sumdiv(n, d, d^n*(gcd(d, n/d) == 1)) % n) == (n-1); \\ Michel Marcus, Sep 30 2014

isok(n) = sumdiv(n, d, if (gcd(d, n/d) == 1, Mod(d, n)^n)) == Mod(n-1, n); \\ Michel Marcus, Oct 02 2014

a(4)-a(5) from Hiroaki Yamanouchi, Sep 30 2014

a(6) from Hiroaki Yamanouchi, Oct 02 2014

cp's OEIS Frontend

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

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