A063784 Primes that are the sum of cubes of divisors of some integer.

73, 757, 1772893, 48551233240513, 378890487846991, 3156404483062657, 17390284913300671, 280343912759041771, 319913861581383373, 487014306953858713, 7824668707707203971, 8443914727229480773, 32564717507686012813, 48095468363380957093, 54811417636756749151

Offset: 1

Author

Labos Elemer, Aug 17 2001

Keywords

• nonn

Comments

Primes of the form p^6 + p^3 + 1 where p is a prime. - Amiram Eldar, Aug 16 2024

Examples

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

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Harry J. Smith)

Crossrefs

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

Programs

Mathematica

Select[Table[p^6 + p^3 + 1, {p, Prime[Range[500]]}], PrimeQ] (* Amiram Eldar, Aug 16 2024 *)

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

Formula

Primes of form p = sigma_3(k).

From Amiram Eldar, Aug 16 2024: (Start)

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

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