A233769 Prime(k), where k is such that (1 + Sum_{i=1..k} prime(i)^19) / k is an integer.

2, 3, 7, 11, 13, 29, 37, 241, 1429, 2437, 2741, 4583, 7333, 8269, 36073, 37397, 48121, 73037, 130261, 147289, 280037, 1032259, 6594787, 10249573, 130193849, 443038781, 527454197, 1024907927, 1736090963, 2602512709, 13517865841, 13684220029, 64209198247, 93380481511, 126718347859, 143176188581, 231059158871, 273286859737, 511940464493, 512760363097, 715173864563, 810985955573

Offset: 1

Author

Robert Price, Dec 15 2013

Keywords

• nonn

Comments

a(51) > 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^19+1 = 1523090798793695143992 when divided by 6 equals 253848466465615857332 which is an integer.
		

Links

• Bruce Garner, Table of n, a(n) for n = 1..50 (first 42 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

t = {}; sm = 1; Do[sm = sm + Prime[n]^19; If[Mod[sm, n] == 0, AppendTo[t, Prime[n]]], {n, 100000}]; t (* Derived from A217599 *)

PARI

is(n)=if(!isprime(n),return(0)); my(t=primepi(n),s); forprime(p=2,n,s+=Mod(p,t)^19); s==0 \\ Charles R Greathouse IV, Nov 30 2013