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%I #26 Feb 21 2024 01:49:15
%S 1,4,8,12,16,20,24,28,32,35,36,40,44,48,52,55,56,60,64,68,72,76,77,80,
%T 84,88,92,95,96,100,104,108,112,115,116,119,120,124,128,132,136,140,
%U 143,144,148,152,155,156,160,161,164,168,172,176,180,184,187,188,192,196,200,203,204
%N Numbers n such that 1^(n-1)+2^(n-1)+...+n^(n-1) == 0 (mod n)
%C 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
%C 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
%H Ivan Neretin, <a href="/A191677/b191677.txt">Table of n, a(n) for n = 1..10000</a>
%t is191677[n_]:=Mod[Sum[PowerMod[k, n - 1, n], {k, 1, n - 1}], n] == 0;
%t Select[Range[300], is191677]
%o (PARI) select( is_A191677(n)=!sum(k=1,n-1,Mod(k,n)^(n-1)), [1..200]) \\ _M. F. Hasler_, Jul 22 2019
%Y Cf. A121707 (n^3 divides Sum_{k<n} k^n).
%K nonn
%O 1,2
%A _José María Grau Ribas_, Jun 10 2011