A232962 Prime(m), where m is such that (Sum_{k=1..m} prime(k)^9) / m is an integer.

2, 3974779, 15681179, 250818839, 6682314181, 9143935289, 311484445891, 718930864213, 1004267651657, 7014674460791, 1745134691306711, 2853623691677477, 9950715071009107

Offset: 1

Author

Robert Price, Dec 02 2013

Keywords

• nonn
• more

Comments

The primes correspond to indices n = 1, 281525, 1011881, 13721649, 309777093, 417800903, 12252701193, 27377813605, 37762351523 = A131263.

a(12) > 1878338967416897. - Paul W. Dyson, Mar 27 2021

a(13) > 3475385758524527. - Bruce Garner, Jan 10 2022

a(14) > 10765720281292199. - Paul W. Dyson, Aug 11 2022

a(14) > 18205684894350047. - Paul W. Dyson, Dec 16 2024

Examples

			a(2) = 3974779, because 3974779 is the 281525th prime and the sum of the first 281525 primes^9 = 6520072223138145034616659509499972547782386874741800687550730350 when divided by 281525 equals 23159833844731888942781847116597007540297973092058611801974 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).

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]^9; 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)^9); s==0 \\ Charles R Greathouse IV, Nov 30 2013

PARI

S=n=0;forprime(p=1,,(S+=p^9)%n++||print1(p",")) \\ M. F. Hasler, Dec 01 2013

Formula

a(n) = prime(A131263(n)). - M. F. Hasler, Dec 01 2013

Extensions

a(10) from Karl-Heinz Hofmann, Jan 24 2021

a(11) from Paul W. Dyson, Mar 27 2021

a(12) from Bruce Garner, Jan 10 2022

a(13) from Paul W. Dyson, Aug 11 2022