A233557 Prime(k), where k is such that (1 + Sum_{i=1..k} prime(i)^17) / k is an integer.

2, 3, 7, 13, 29, 37, 641, 853, 2143, 18059, 26417, 34283, 48539, 122597, 146539, 254831, 8304757, 19534651, 26528699, 32820527, 47825363, 82199141, 124088207, 312168289, 409464961, 464174839, 1167927947, 1393486043, 1725361103, 1879982849, 4346448019, 7331901341, 7451088943, 27036461983, 39662532977, 113692593373, 449281234057

Offset: 1

Author

Robert Price, Dec 12 2013

Keywords

• nonn

Comments

a(45) > 491952295618219. - Bruce Garner, Jun 02 2021

Examples

			13 is a term because 13 is the 6th prime and the sum of the first 6 primes^17+1 = 9156096341463343272 when divided by 6 equals 1526016056910557212 which is an integer.
		

Links

• Bruce Garner, Table of n, a(n) for n = 1..44 (first 37 terms from Robert Price, terms 38..39 from Karl-Heinz Hofmann)
• 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

t = {}; sm = 1; Do[sm = sm + Prime[n]^17; If[Mod[sm, n] == 0, AppendTo[t, Prime[n]]], {n, 100000}]; t (* Derived from A217599 *)
With[{nn=175*10^8},Prime[#]&/@Select[Thread[{Range[nn],Accumulate[ Prime[ Range[nn]]^17]}],Divisible[#[[2]]+1,#[[1]]]&][[All,1]]] (* The program will take a long time to run *) (* Harvey P. Dale, Apr 13 2018 *)

PARI

is(n)=if(!isprime(n),return(0)); my(t=primepi(n),s); forprime(p=2,n,s+=Mod(p,t)^17); s==0 \\ Charles R Greathouse IV, Nov 30 2013