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%I #28 Feb 02 2019 03:19:37
%S 9,21,25,33,45,49,57,65,69,81,93,105,117,121,129,133,141,145,153,165,
%T 169,177,185,189,201,213,217,225,237,249,261,265,273,285,289,297,301,
%U 305,309,321,333,341,345,357,361,369,381,385,393,405,417,425,429,441,453,465,469,477,481,489,501,505,513,525,529,537
%N Odd numbers k such that 1^((k-1)/2) + 2^((k-1)/2) + ... + (k-1)^((k-1)/2) <> 0 (mod k).
%H Charles R Greathouse IV, <a href="/A188159/b188159.txt">Table of n, a(n) for n = 1..10000</a>
%H J. M. Grau, Florian Luca, Antonio M. Oller-Marcen, <a href="https://arxiv.org/abs/1103.3428">On a variant of Giuga numbers</a>, arXiv:1103.3428 [math.NT], 2011.
%p isA188159 := proc(n) if type(n,'odd') then add( i^((n-1)/2),i=1..n-1) ; is(% mod n <>0 ); else false; end if; end proc:
%p for n from 1 to 350 by 2 do if isA188159(n) then printf("%d,",n) ; end if; end do: # _R. J. Mathar_, Mar 30 2011
%t okQ[n_] := Mod[Sum[PowerMod[j,(n-1)/2,n], {j,n-1}], n]==0; Select[Range[1,1000,2], okQ]
%o (PARI) is(n)=if(n%2==0,return(0));my(e=(n-1)/2);sum(k=1,n-1,Mod(k,n)^e)!=0 \\ _Charles R Greathouse IV_, Feb 04 2013
%K nonn
%O 1,1
%A _José María Grau Ribas_, Mar 28 2011
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