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

Author

José María Grau Ribas, Jun 10 2011

Keywords

• nonn

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_{kM. F. Hasler, Jul 22 2019

Links

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

Crossrefs

Cf. A121707 (n^3 divides Sum_{k

Programs

Mathematica

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

PARI

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

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