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A223936 Numbers prime(m), such that (Sum_{i=1..m} prime(i)^3) / m is an integer. 2
2, 97, 3877, 4943, 50741, 1487159, 3356117, 131047091863, 449627893189, 906460844407, 61168531626487, 141835115384731, 749668095960389, 1259394274876189, 3849791511371129, 6669425423437787, 11674340378841221 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

a(12) > 64343047069687. - Paul W. Dyson, Jan 05 2021

a(13) > 158308642985671. - Bruce Garner, Mar 01 2021

a(14) > 764476112423819. - Bruce Garner, Apr 06 2021

a(15) > 1352363608564489. - Bruce Garner, May 13 2021

a(16) > 5275749137419261. - Bruce Garner, Jan 08 2022

a(17) > 12244897030891601. - Bruce Garner, Jul 31 2022

LINKS

Table of n, a(n) for n=1..17.

OEIS Wiki, Sums of powers of primes divisibility sequences

EXAMPLE

a(2) = 97, because 97 is the 25th prime and the sum of the first 25 primes^3 = 4696450 when divided by 25 equals 187858 which is an integer.

MATHEMATICA

k = 1; p = 2; s = 0; lst = {}; While[p < 1000000000, s = s + p^3; If[ Mod[s, k++] == 0, AppendTo[lst, p]]; p = NextPrime@ p]; lst

CROSSREFS

Cf. A085450 (smallest m > 1 that 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: A233192 A065592 A233767 * A224083 A285023 A232865

Adjacent sequences: A223933 A223934 A223935 * A223937 A223938 A223939

KEYWORD

nonn,more

AUTHOR

Robert Price, Mar 29 2013

EXTENSIONS

a(11) from Paul W. Dyson, Jan 05 2021

a(12) from Bruce Garner, Mar 01 2021

a(13) from Bruce Garner, Apr 06 2021

a(14) from Bruce Garner, May 13 2021

a(15) from Bruce Garner, Jan 08 2022

a(16) from Paul W. Dyson, Jan 17 2022

a(17) from Bruce Garner, Jul 31 2022

STATUS

approved

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Last modified January 28 18:12 EST 2023. Contains 359895 sequences. (Running on oeis4.)