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A232733 Prime(n), where n is such that (sum_{i=1..n} prime(i)^6) / n is an integer. 0
2, 41647, 3197891, 630397289, 779089704751 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

a(6) > 1121614951687.

The primes correspond to indices n = 1, 4357, 230065, 32826947, 29578097627 = A125825.

LINKS

Table of n, a(n) for n=1..5.

OEIS Wiki, Sums of powers of primes divisibility sequences

FORMULA

a(n) = prime(A125828(n)).

EXAMPLE

a(2) = 41647, because 41647 is the 4357th prime and the sum of the first 4357 primes^6 = 2952411812082729747782733271068 when divided by 4357 equals 677624928180566845945084524 which is an integer.

MATHEMATICA

t = {}; sm = 0; Do[sm = sm + Prime[n]^6; 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)^6); s==0 \\ Charles R Greathouse IV, Nov 30 2013

(PARI) S=n=0; forprime(p=1, , (S+=p^6)%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: A257968 A303738 A055578 * A106025 A157959 A290047

Adjacent sequences:  A232730 A232731 A232732 * A232734 A232735 A232736

KEYWORD

nonn,more

AUTHOR

Robert Price, Dec 02 2013

STATUS

approved

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Last modified April 19 18:37 EDT 2019. Contains 322290 sequences. (Running on oeis4.)