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A223936
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Numbers prime(m), such that (Sum_{i=1..m} prime(i)^3) / m is an integer.
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2
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2, 97, 3877, 4943, 50741, 1487159, 3356117, 131047091863, 449627893189, 906460844407, 61168531626487, 141835115384731, 749668095960389, 1259394274876189, 3849791511371129, 6669425423437787, 11674340378841221
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OFFSET
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1,1
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COMMENTS
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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
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LINKS
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Table of n, a(n) for n=1..17.
OEIS Wiki, Sums of powers of primes divisibility sequences
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EXAMPLE
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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.
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MATHEMATICA
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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
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CROSSREFS
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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
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KEYWORD
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nonn,more
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AUTHOR
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Robert Price, Mar 29 2013
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EXTENSIONS
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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
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STATUS
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approved
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