A233863 Prime(n), where n is such that (1 + Sum_{i=1..n} prime(i)^3) / n is an integer.

2, 3, 7, 11, 13, 29, 37, 43, 257, 421, 449, 7333, 7673, 9433, 9539, 12163, 53551, 74759, 119429, 199909, 295703, 2494781, 6941633, 39150679, 50026091, 165204709, 410054731, 724768817, 1282680871, 1777452847, 2923304383, 6053209493, 7423469173, 35896955599, 46936773853

Offset: 1

Author

Robert Price, Dec 16 2013

Keywords

• nonn

Comments

a(50) > 730228645826551. - Bruce Garner, Apr 04 2021

a(55) > 7824556240506443. - Bruce Garner, Mar 28 2022

Examples

			a(5) = 13, because 13 is the 6th prime and the sum of the first 6 primes^3+1 = 4032 when divided by 6 equals 672 which is an integer.
		

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

t = {}; sm = 1; Do[sm = sm + Prime[n]^3; If[Mod[sm, n] == 0, AppendTo[t, Prime[n]]], {n, 100000}]; t (* Derived from A217599 *)
Module[{nn=7500,pt},pt=1+Accumulate[Prime[Range[nn]]^3];Prime[#]&/@ Select[ Thread[{pt,Range[nn]}],Divisible[#[[1]],#[[2]]]&]][[All,2]] (* The program generates the first 18 terms of the sequence. It is not suitable for generating many more. *) (* Harvey P. Dale, Mar 17 2022 *)

PARI

is(n)=if(!isprime(n),return(0)); my(t=primepi(n),s); forprime(p=2,n,s+=Mod(p,t)^3); s==0 \\ Charles R Greathouse IV, Nov 30 2013