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Numbers m that divide 2^6 + 3^6 + 5^6 + ... + prime(m)^6.
2

%I #44 Dec 08 2022 07:38:01

%S 1,4357,230065,32826947,29578097627,136736829787,1449657373945,

%T 39153480154471,275533558444523,442844575927975,879110348271737

%N Numbers m that divide 2^6 + 3^6 + 5^6 + ... + prime(m)^6.

%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]^6; If[ Mod[s, n] == 0, Print[n]], {n, 240000}]

%o (PARI) s=0;n=0;forprime(p=2,4e9,s+=p^6;if(s%n++==0,print1(n", "))) \\ _Charles R Greathouse IV_, Mar 15 2011

%Y Cf. A236182.

%K nonn,hard,more

%O 1,2

%A _Alexander Adamchuk_, Feb 03 2007

%E a(4) from _Stefan Steinerberger_, May 10 2007

%E a(5)-a(6) from _Charles R Greathouse IV_, Mar 15 2011 to Mar 19 2011

%E a(7) from _Paul W. Dyson_, Jan 08 2021

%E a(8) from _Bruce Garner_, Jul 10 2021

%E a(9) from _Paul W. Dyson_, Oct 21 2022

%E a(10) from _Paul W. Dyson_, Oct 31 2022

%E a(11) from _Paul W. Dyson_, Dec 08 2022