

A191677


Numbers n such that 1^(n1)+2^(n1)+...+n^(n1) == 0 (mod n)


9



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
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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


MAPLE

select(n>frac((add(k^(n1), k=1..n))/n)=0, [$1..204]); # Paolo P. Lava, May 14 2019


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, n1, Mod(k, n)^(n1)), [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 A295774
Adjacent sequences: A191674 A191675 A191676 * A191678 A191679 A191680


KEYWORD

nonn


AUTHOR

José María Grau Ribas, Jun 10 2011


STATUS

approved



