A063784 - OEIS

%I #27 Aug 16 2024 21:19:18

%S 73,757,1772893,48551233240513,378890487846991,3156404483062657,

%T 17390284913300671,280343912759041771,319913861581383373,

%U 487014306953858713,7824668707707203971,8443914727229480773,32564717507686012813,48095468363380957093,54811417636756749151

%N Primes that are the sum of cubes of divisors of some integer.

%C Primes of the form p^6 + p^3 + 1 where p is a prime. - _Amiram Eldar_, Aug 16 2024

%H Amiram Eldar, <a href="/A063784/b063784.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from Harry J. Smith)

%F Primes of form p = sigma_3(k).

%F From _Amiram Eldar_, Aug 16 2024: (Start)

%F a(n) = A001158(A063783(n)).

%F a(n) = A060883(A066100(n)). (End)

%e sigma_3(9) = 1 + 27 + 729 = 757, a prime.

%t Select[Table[p^6 + p^3 + 1, {p, Prime[Range[500]]}], PrimeQ] (* _Amiram Eldar_, Aug 16 2024 *)

%o (PARI) { n=0; p=0; for (m=1, 10^9, p=nextprime(p+1); if(isprime(q=p^6 + p^3 + 1), write("b063784.txt", n++, " ", q); if (n==1000, break)) ) } \\ _Harry J. Smith_, Aug 31 2009

%Y Cf. A001158, A023194, A060883, A063783, A066100.

%K nonn

%O 1,1

%A _Labos Elemer_, Aug 17 2001