A233133 Numbers k such that k divides 1 + Sum_{j=1..k} prime(j)^10.

1, 2, 3, 4, 6, 8, 9, 11, 12, 13, 22, 24, 26, 27, 33, 44, 45, 48, 66, 71, 76, 88, 107, 132, 148, 168, 176, 187, 207, 216, 264, 330, 360, 418, 440, 462, 528, 672, 864, 880, 1056, 1221, 1276, 1304, 1340, 1408, 1465, 1531, 1672, 1683, 2153, 2374, 2760, 3520

Offset: 1

Author

Robert Price, Dec 04 2013

Keywords

• nonn

Comments

a(211) > 3.0*10^13. - Bruce Garner, Jun 06 2021

Examples

			a(5)=6 because 1 plus the sum of the first 6 primes^10 is 164088217398 which is divisible by 6.
		

Links

• Bruce Garner, Table of n, a(n) for n = 1..210 (first 174 terms from Robert Price)
• 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 < 41000000000, s = s + p^10; If[Mod[s, ++k] == 0, AppendTo[lst, k]; Print[{k, p}]]; p = NextPrime@ p] (* derived from A128169 *)
Module[{nn=3600,sp},sp=Accumulate[Prime[Range[nn]]^10];Select[ Range[ nn],Divisible[ sp[[#]]+1,#]&]] (* Harvey P. Dale, Sep 18 2018 *)