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A232962 Prime(n), where n is such that (sum_{i=1..n} prime(i)^9) / n is an integer. 0
2, 3974779, 15681179, 250818839, 6682314181, 9143935289, 311484445891, 718930864213, 1004267651657 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

a(10) > 1066173339601.

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

LINKS

Table of n, a(n) for n=1..9.

OEIS Wiki, Sums of powers of primes divisibility sequences

FORMULA

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

EXAMPLE

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.

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 *)

PROG

(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

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.

Sequence in context: A214599 A071066 A137601 * A158347 A273354 A157991

Adjacent sequences:  A232959 A232960 A232961 * A232963 A232964 A232965

KEYWORD

nonn,more

AUTHOR

Robert Price, Dec 02 2013

STATUS

approved

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Last modified October 21 19:29 EDT 2019. Contains 328315 sequences. (Running on oeis4.)