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Numbers m that divide 2^11 + 3^11 + 5^11 + ... + prime(m)^11.
2

%I #40 Jan 03 2023 05:43:42

%S 1,25,59,2599,6195,421407,11651191,19293221,255136097,1820015683,

%T 2183556659,7993872143,9850779563,2006892138335,2649677145789,

%U 6645858099781,318039538085101

%N Numbers m that divide 2^11 + 3^11 + 5^11 + ... + prime(m)^11.

%C a(17) > 8*10^12. - _Bruce Garner_, Mar 29 2021

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

%t s = 0; Do[s = s + Prime[n]^11; If[ Mod[s, n] == 0, Print[n]], {n, 7000}]

%o (PARI) s=0; n=0; forprime(p=2, 4e9, s+=p^11; if(s%n++==0, print1(n", "))) \\ _Charles R Greathouse IV_, Mar 20 2011

%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,more,nonn

%O 1,2

%A _Alexander Adamchuk_, Feb 03 2007

%E 3 more terms from _Stefan Steinerberger_, Jun 06 2007

%E 1 more term from _Sean A. Irvine_, Jan 26 2011

%E a(10)-a(13) from _Charles R Greathouse IV_, Mar 20 2011

%E a(14) from _Paul W. Dyson_, Jan 08 2021

%E a(15) from _Bruce Garner_, Mar 08 2021

%E a(16) from _Bruce Garner_, Mar 29 2021

%E a(17) from _Paul W. Dyson_, Jan 03 2023