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A232963 Prime(n), where n is such that (sum_{i=1..n} prime(i)^14) / n is an integer. 0
2, 1933, 3217, 41681, 114311, 2743691233, 7252463461 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

a(8) > 1093881323023.

The primes correspond to indices n = 1, 295, 455, 4361, 10817, 132680789, 334931875 = A131274.

LINKS

Table of n, a(n) for n=1..7.

OEIS Wiki, Sums of powers of primes divisibility sequences

FORMULA

a(n) = prime(A131274(n)).

EXAMPLE

a(2) = 1933, because 1193391 is the 295th prime and the sum of the first 295 primes^14 = 172657243368537051859007103457435197295421033550 when divided by 295 equals 585278791079786616471210520194695584052274690 which is an integer.

MATHEMATICA

t = {}; sm = 0; Do[sm = sm + Prime[n]^14; 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)^14); s==0 \\ Charles R Greathouse IV, Nov 30 2013

(PARI) S=n=0; forprime(p=1, , (S+=p^14)%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: A230082 A217372 A160299 * A238119 A177188 A125635

Adjacent sequences:  A232960 A232961 A232962 * A232964 A232965 A232966

KEYWORD

nonn,more

AUTHOR

Robert Price, Dec 02 2013

STATUS

approved

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Last modified August 17 11:06 EDT 2019. Contains 326057 sequences. (Running on oeis4.)