A232848 Prime(k), where k divides Sum_{i=1..k} prime(i)^15.

2, 59, 97, 127, 12517, 54581, 83921, 89273, 1396411, 2562719, 4952183, 29201281, 35562101, 47567557, 111213143, 184201627, 1172476337, 7309217299, 287609314877, 5173838081669, 408907258717171, 1357729730868191, 66413899001789557

Offset: 1

Author

Robert Price, Dec 09 2013

Keywords

• nonn
• more

Examples

			a(2) = 59, because 59 is the 17th prime and the sum of the first 17 primes^15 = 455708280934100194626604550 when divided by 17 equals 26806369466711776154506150 which is an integer.
		

Links

• 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), A131275.

Cf. A007504, A045345, A171399, A128165, A233523, A050247, A050248.

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

Programs

Mathematica

t = {}; sm = 0; Do[sm = sm + Prime[n]^15; 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)^15); s==0 \\ Charles R Greathouse IV, Nov 30 2013

PARI

S=n=0;forprime(p=1,,(S+=p^15)%n++||print1(p",")) \\ M. F. Hasler, Dec 01 2013

Formula

a(n) = prime(A131275(n)).

Extensions

a(20) from Karl-Heinz Hofmann, Feb 17 2021

a(21) from Bruce Garner, Apr 30 2021

a(22) from Bruce Garner, Jan 07 2022

a(23) from Paul W. Dyson, Apr 18 2024