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%I #43 Mar 29 2022 08:46:41
%S 1,2,4,5,6,10,12,14,55,82,87,935,973,1168,1181,1457,5457,7372,11250,
%T 17978,25664,182717,472931,2385026,3002594,9249715,21843515,37468158,
%U 64403264,87803374,140933482,281907048,342460116,1543515106,1995156064
%N Numbers k such that k divides 1 + Sum_{j=1..k} prime(j)^3 = 1 + A098999(k).
%C a(55) > 2.2*10^14. - _Bruce Garner_, Mar 28 2022
%H Bruce Garner, <a href="/A128167/b128167.txt">Table of n, a(n) for n = 1..54</a>
%H OEIS Wiki, <a href="https://oeis.org/wiki/Sums_of_primes_divisibility_sequences">Sums of powers of primes divisibility sequences</a>
%t k = 0; s = 1; p = 2; lst = {}; While[k < 516862000, s = s + p^3; If[Mod[s, ++k] == 0, AppendTo[lst, k]; Print[{k, p}]]; p = NextPrime@ p]; lst
%Y Cf. A085450 = smallest m > 1 such that m divides Sum_{k=1..m} prime(k)^n.
%Y Cf. A007504, A045345, A171399, A128165, A233523, A050247, A050248.
%Y Cf. A024450, A111441, A217599, A128166, A233862, A217600, A217601.
%K hard,nonn
%O 1,2
%A _Alexander Adamchuk_, Feb 22 2007, Feb 23 2007
%E Four more terms from _Sean A. Irvine_, Jan 19 2011
%E a(32) & a(33) from _Robert G. Wilson v_
%E a(34)-a(35) from _Robert Price_, Dec 16 2013
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