A120808 Integers p such that x = p^3 is in A120806: x+d+1 is prime for all divisors d of x. All p greater than 1 are odd primes.

1, 5, 71, 303839, 1030349, 1356899, 1437719, 2248529, 2416259, 2576549, 2797961, 4007321, 4353521, 4875491, 6137501, 6611441, 6698831, 6904421, 7821791, 8078981, 9221231, 9311279, 9500279, 10157309, 11251421, 11879939, 11957969, 12040751, 13906649, 15299021, 16043369

Offset: 1

Author

Walter Kehowski, Jul 06 2006

Keywords

• nonn

Examples

			a(3) = 71 since x = 71^3 = 357911, divisors(x) = {1, 71, 71^2, 71^3} and x+d+1 = {357913, 357983, 362953, 715823} are all primes.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..2500

Crossrefs

Cf. A120806, A120807.

Programs

Maple

L:=[]: for w to 1 do for k from 1 while nops(L)<=50 do p:=ithprime(k); x:=p^3; if p mod 6 = 5 and andmap(isprime,[x+2,2*x+1]) then S:={p,p^2}; Q:=map(z-> x+z+1, S); if andmap(isprime,Q) then L:=[op(L),x]; print(nops(L),p,x); fi; fi; od od;

PARI

is(k) = {my(x=k^3); k == 1 || (isprime(k) && isprime(x+2) && isprime(x+k+1) && isprime(x+k^2+1) && isprime(2*x+1));} \\ Amiram Eldar, Aug 05 2024

Formula

a(1) = 1. a(n) = p where p is the (n-1)-st prime such that x = p^3 is in A120806: x+d+1 is prime for all divisors d of x.

Extensions

a(28)-a(31) from Amiram Eldar, Aug 05 2024