A128167 Numbers k such that k divides 1 + Sum_{j=1..k} prime(j)^3 = 1 + A098999(k).

1, 2, 4, 5, 6, 10, 12, 14, 55, 82, 87, 935, 973, 1168, 1181, 1457, 5457, 7372, 11250, 17978, 25664, 182717, 472931, 2385026, 3002594, 9249715, 21843515, 37468158, 64403264, 87803374, 140933482, 281907048, 342460116, 1543515106, 1995156064

Offset: 1

Author

Alexander Adamchuk, Feb 22 2007, Feb 23 2007

Keywords

• hard
• nonn

Comments

a(55) > 2.2*10^14. - Bruce Garner, Mar 28 2022

Links

• Bruce Garner, Table of n, a(n) for n = 1..54
• 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

k = 0; s = 1; p = 2; lst = {}; While[k < 516862000, s = s + p^3; If[Mod[s, ++k] == 0, AppendTo[lst, k]; Print[{k, p}]]; p = NextPrime@ p]; lst

Extensions

Four more terms from Sean A. Irvine, Jan 19 2011

a(32) & a(33) from Robert G. Wilson v

a(34)-a(35) from Robert Price, Dec 16 2013