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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, 75041264698436783
OFFSET
1,1
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).
Sequence in context: A233192 A065592 A233767 * A224083 A285023 A232865
KEYWORD
nonn,more,changed
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
a(18) from Paul W. Dyson, Feb 18 2024
STATUS
approved