A128169 - OEIS

%I #44 Mar 29 2022 08:48:22

%S 1,2,4,6,10,12,22,58,155,363,464,665,1146,2870,3048,4019,5931,8724,

%T 21503,50439,67560,476281,705570,4050684,6956459,7443590,10449928,

%U 10799546,15385564,17735139,83325458,245271750,255583775,1395860516,2921734534,6255577368,9050771725,12062893218,13689205205,42254229197,46440930382

%N Numbers k such that k divides 1 + Sum_{j=1..k} prime(j)^5 = 1 + A122103(k).

%C a(52) > 3*10^13. - _Bruce Garner_, Jun 05 2021

%C a(53) > 1.2*10^14. - _Bruce Garner_, Mar 28 2022

%H Bruce Garner, <a href="/A128169/b128169.txt">Table of n, a(n) for n = 1..52</a>

%H OEIS Wiki, <a href="https://oeis.org/wiki/Sums_of_primes_divisibility_sequences">Sums of powers of primes divisibility sequences</a>

%t p = 2; k = 0; s = 1; lst = {}; While[k < 521330000, s = s + p^5; If[Mod[s, ++k] == 0, AppendTo[lst, k]; Print[{k, p}]]; p = NextPrime@ p]

%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 a(31) from _Sean A. Irvine_, Jan 19 2011

%E a(32)-a(33) from _Robert G. Wilson v_, Jan 20 2011

%E a(34)-a(41) from _Robert Price_, Dec 18 2013