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

1,2

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.

Mathematica

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

Prog

(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

Crossrefs

Cf. A007850.

Sequence in context: A322840 A336374 A346669 * A272872 A359080 A103796

Adjacent sequences: A187926 A187927 A187928 * A187930 A187931 A187932

Keyword

nonn

Author

José María Grau Ribas, Mar 16 2011

Status

approved