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A223936
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Prime(m), where m is 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
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history;
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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
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LINKS
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Table of n, a(n) for n=1..14.
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
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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
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STATUS
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approved
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