login
A238983
Numbers n such that the sum of n-th powers of unitary divisors of n is congruent to -1 modulo n.
2
1, 2, 265, 49217, 7870171, 592258417
OFFSET
1,2
COMMENTS
a(7) > 10^10. - Hiroaki Yamanouchi, Oct 02 2014
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 &]
PROG
(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
CROSSREFS
KEYWORD
nonn,more,hard
AUTHOR
EXTENSIONS
a(4)-a(5) from Hiroaki Yamanouchi, Sep 30 2014
a(6) from Hiroaki Yamanouchi, Oct 02 2014
STATUS
approved