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A238983 Numbers n such that the sum of n-th powers of unitary divisors of n is congruent to -1 modulo n. 2

%I

%S 1,2,265,49217,7870171,592258417

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

%C a(7) > 10^10. - _Hiroaki Yamanouchi_, Oct 02 2014

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

%o (PARI) isok(n) = (sumdiv(n, d, d^n*(gcd(d, n/d) == 1)) % n) == (n-1); \\ _Michel Marcus_, Sep 30 2014

%o (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

%Y Cf. A034448, A238981, A238982.

%K nonn,more,hard

%O 1,2

%A _José María Grau Ribas_, Mar 07 2014

%E a(4)-a(5) from _Hiroaki Yamanouchi_, Sep 30 2014

%E a(6) from _Hiroaki Yamanouchi_, Oct 02 2014

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Last modified March 22 12:43 EDT 2019. Contains 321421 sequences. (Running on oeis4.)