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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. 3
1, 125, 357911, 28049850707778719, 1093838138707598549, 2498288375480240699, 2971816820123565959, 11368298790243739889, 14106863174732461979, 17104690428464397149, 21904077634699214681, 64352051556875937161 (list; graph; refs; listen; history; text; internal format)
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

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Last modified November 27 03:16 EST 2021. Contains 349345 sequences. (Running on oeis4.)