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

1, 2, 265, 49217, 7870171, 592258417

Offset: 1

Author

José María Grau Ribas, Mar 07 2014

Keywords

• nonn
• more
• hard

Comments

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

Crossrefs

Cf. A034448, A238981, A238982.

Programs

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

PARI

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

PARI

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

Extensions

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

a(6) from Hiroaki Yamanouchi, Oct 02 2014