A128165 Numbers k such that k divides 1 plus the sum of the first k primes.

1, 2, 6, 10, 20, 22, 28, 155, 488, 664, 992, 6162, 7840, 7975, 8793, 18961, 32422, 148220, 231625, 332198, 459121, 462932, 2115894, 8108930, 10336641, 11789731, 15500046, 23483195, 46571611, 48582404, 77033887, 105390951, 132421841, 229481560, 1224959312

Offset: 1

Author

Alexander Adamchuk, Feb 22 2007

Keywords

• hard
• nonn

Comments

a(44) > 4.4*10^10. - Robert Price, Dec 15 2013

a(50) > 10^14. - Bruce Garner, Jun 05 2021

Links

• Bruce Garner, Table of n, a(n) for n = 1..49
• OEIS Wiki, Sums of powers of primes divisibility sequences

Crossrefs

Cf. A085450 (smallest m > 1 such that m divides Sum_{k=1..m} prime(k)^n).

Cf. A007504, A045345, A171399, A128165, A233523, A050247, A050248, A024450, A111441, A217599, A128166, A233862, A217600, A217601.

Programs

Mathematica

k = 0; s = 1; p = 2; A128165 = {}; While[k < 247336000, If[Mod[s += p, ++k] == 0, AppendTo[A128165, k]; Print[{k, p}]]; p = NextPrime@ p]; A128165

PARI

is(n)=sum(i=1,n,prime(i),1)%n==0 \\ Charles R Greathouse IV, Nov 07 2014

PARI

n=0; s=1; forprime(p=2,1e9, s+=p; if(s%n++==0, print1(n", "))) \\ Charles R Greathouse IV, Nov 07 2014

Extensions

More terms from Ryan Propper, Apr 05 2007

a(34) from Robert G. Wilson v, Jan 21 2011

a(35) from Robert Price, Dec 15 2013