A120807 Cubes in A120806: n+d+1 is prime for all divisors d of n. All cubes greater than 1 are cubes of odd primes.

1, 125, 357911, 28049850707778719, 1093838138707598549, 2498288375480240699, 2971816820123565959, 11368298790243739889, 14106863174732461979, 17104690428464397149, 21904077634699214681, 64352051556875937161

Offset

1,2

Links

Table of n, a(n) for n=1..12.

Formula

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

Example

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

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;

Mathematica

Select[Range[4008000]^3, AllTrue[#+Divisors[#]+1, PrimeQ]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, May 26 2019 *)

Crossrefs

Cf. A120806, A120808.

Sequence in context: A161354 A318258 A003751 * A013836 A048563 A239060

Adjacent sequences: A120804 A120805 A120806 * A120808 A120809 A120810

Keyword

nonn

Author

Walter Kehowski, Jul 06 2006

Status

approved