A188159 Odd numbers k such that 1^((k-1)/2) + 2^((k-1)/2) + ... + (k-1)^((k-1)/2) <> 0 (mod k).

9, 21, 25, 33, 45, 49, 57, 65, 69, 81, 93, 105, 117, 121, 129, 133, 141, 145, 153, 165, 169, 177, 185, 189, 201, 213, 217, 225, 237, 249, 261, 265, 273, 285, 289, 297, 301, 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

Offset

1,1

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

J. M. Grau, Florian Luca, Antonio M. Oller-Marcen, On a variant of Giuga numbers, arXiv:1103.3428 [math.NT], 2011.

Maple

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:
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

Mathematica

okQ[n_] := Mod[Sum[PowerMod[j, (n-1)/2, n], {j, n-1}], n]==0; Select[Range[1, 1000, 2], okQ]

Prog

(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

Crossrefs

Sequence in context: A210251 A143791 A091113 * A272600 A359161 A327862

Adjacent sequences: A188156 A188157 A188158 * A188160 A188161 A188162

Keyword

nonn

Author

José María Grau Ribas, Mar 28 2011

Status

approved