A187929 Odd numbers k such that 1^((k-1)/2) + 2^((k-1)/2) + .... + (k-1)^((k-1)/2) == 0 (mod k).

1, 3, 5, 7, 11, 13, 15, 17, 19, 23, 27, 29, 31, 35, 37, 39, 41, 43, 47, 51, 53, 55, 59, 61, 63, 67, 71, 73, 75, 77, 79, 83, 85, 87, 89, 91, 95, 97, 99, 101, 103, 107, 109, 111, 113, 115, 119, 123, 125, 127, 131, 135, 137, 139, 143, 147, 149, 151, 155, 157, 159

Offset: 1

Author

José María Grau Ribas, Mar 16 2011

Keywords

• nonn

Comments

Asymptotic density is 0.379...

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• José María Grau, Florian Luca and Antonio M. Oller-Marcén, On a variant of Giuga numbers, Acta Mathematica Sinica, English Series, Vol. 28 No. 4 (2012), pp 653-660; preprint, arXiv:1103.3428 [math.NT], 2011.

Crossrefs

Cf. A007850.

Programs

Mathematica

gi[n_]:=Mod[Sum[PowerMod[j,(n-1)/2,n],{j,n-1}],n]; Select[ Range[1,300,2], gi[#]==0&]

PARI

is(n)=my(e=(n-1)/2);sum(k=1,n-1,Mod(k,n)^e)==0;
select(is,vector(1000,i,2*i-1)) \\ on older versions, switch the arguments
\\ Charles R Greathouse IV, Mar 19 2011