A097961 Numbers k such that the sum of the first k odd primes is divisible by k.

1, 2, 3, 60, 73, 357, 690, 970, 1560, 1844, 2016, 2071, 3267, 7034, 22388, 37244, 137166, 808334, 1126996, 3420839, 4971830, 14647946, 15553569, 21957090, 31327140, 90514444, 98576118, 204198604, 210662116, 553825420, 1395717645, 2820805440, 6780317160

Offset: 1

Author

Anne M. Donovan (anned3005(AT)aol.com), Oct 22 2004

Keywords

• easy
• nonn

Examples

			a(1) = 1 since 3 is divisible by 1.
a(2) = 2 since 3 + 5 = 8 is divisible by 2.
a(3) = 3 since 3 + 5 + 7 = 15 is divisible by 3.
a(4) != 4 since 3 + 5 + 7 + 11 = 26 is not divisible by 4.
98576118 * 977748014 = 96382603602329652.
		

Crossrefs

Cf. A071148, A363477.

Programs

Mathematica

NextPrim[n_] := Block[{k = n + 1}, While[ !PrimeQ[k], k++ ]; k]; p = 2; s = 0; Do[p = NextPrim[p]; s = s + p; If[ Mod[s, n] == 0, Print[n]], {n, 151666666}] (* Robert G. Wilson v, Oct 23 2004 *)

Python

from sympy import sieve
L = sieve.primerange(3, 1.7*10**11); s, k = 0, 0
for p in L:
    s += p;  k += 1
if s%k == 0: print(k, end = ", ")  # Ya-Ping Lu, Jun 16 2023

Formula

Numbers k such that A071148(k)/k or (A007504(k+1)-2)/k is an integer.

Sum_{i=1..a(n)} prime(i) = n*A363477(n). - Ya-Ping Lu, Jun 16 2023

Extensions

More terms from Robert G. Wilson v, Oct 23 2004

a(28)-a(30) from Rémy Sigrist, Sep 25 2016

a(31)-a(33) from Ya-Ping Lu, Jun 16 2023