A191677 Numbers n such that 1^(n-1)+2^(n-1)+...+n^(n-1) == 0 (mod n)

1, 4, 8, 12, 16, 20, 24, 28, 32, 35, 36, 40, 44, 48, 52, 55, 56, 60, 64, 68, 72, 76, 77, 80, 84, 88, 92, 95, 96, 100, 104, 108, 112, 115, 116, 119, 120, 124, 128, 132, 136, 140, 143, 144, 148, 152, 155, 156, 160, 161, 164, 168, 172, 176, 180, 184, 187, 188, 192, 196, 200, 203, 204

Offset

1,2

Comments

Fermat's little theorem shows that this sequence contains no primes. Related to Giuga's conjecture that the sum is -1 iff n is prime. - Charles R Greathouse IV, Jun 10 2011

Is this is the disjoint union of all multiples of 4 and {1} and A121707 (n^3 divides Sum_{k<n} k^n)? - M. F. Hasler, Jul 22 2019

Links

Ivan Neretin, Table of n, a(n) for n = 1..10000

Mathematica

is191677[n_]:=Mod[Sum[PowerMod[k, n - 1, n], {k, 1, n - 1}], n] == 0;
Select[Range[300], is191677]

Prog

(PARI) select( is_A191677(n)=!sum(k=1, n-1, Mod(k, n)^(n-1)), [1..200]) \\ M. F. Hasler, Jul 22 2019

Crossrefs

Cf. A121707 (n^3 divides Sum_{k<n} k^n).

Sequence in context: A328251 A276079 A311124 * A076310 A161352 A337080

Adjacent sequences: A191674 A191675 A191676 * A191678 A191679 A191680

Keyword

nonn

Author

José María Grau Ribas, Jun 10 2011

Status

approved