A128169 Numbers k such that k divides 1 + Sum_{j=1..k} prime(j)^5 = 1 + A122103(k).

1, 2, 4, 6, 10, 12, 22, 58, 155, 363, 464, 665, 1146, 2870, 3048, 4019, 5931, 8724, 21503, 50439, 67560, 476281, 705570, 4050684, 6956459, 7443590, 10449928, 10799546, 15385564, 17735139, 83325458, 245271750, 255583775, 1395860516, 2921734534, 6255577368, 9050771725, 12062893218, 13689205205, 42254229197, 46440930382

Offset: 1

Author

Alexander Adamchuk, Feb 22 2007, Feb 23 2007

Keywords

• hard
• nonn

Comments

a(52) > 3*10^13. - Bruce Garner, Jun 05 2021

a(53) > 1.2*10^14. - Bruce Garner, Mar 28 2022

Links

• Bruce Garner, Table of n, a(n) for n = 1..52
• 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.

Cf. A024450, A111441, A217599, A128166, A233862, A217600, A217601.

Programs

Mathematica

p = 2; k = 0; s = 1; lst = {}; While[k < 521330000, s = s + p^5; If[Mod[s, ++k] == 0, AppendTo[lst, k]; Print[{k, p}]]; p = NextPrime@ p]

Extensions

a(31) from Sean A. Irvine, Jan 19 2011

a(32)-a(33) from Robert G. Wilson v, Jan 20 2011

a(34)-a(41) from Robert Price, Dec 18 2013