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%I #4 May 26 2019 22:16:13
%S 1,125,357911,28049850707778719,1093838138707598549,
%T 2498288375480240699,2971816820123565959,11368298790243739889,
%U 14106863174732461979,17104690428464397149,21904077634699214681,64352051556875937161
%N Cubes in A120806: n+d+1 is prime for all divisors d of n. All cubes greater than 1 are cubes of odd primes.
%F 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).
%e 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.
%p 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;
%t Select[Range[4008000]^3,AllTrue[#+Divisors[#]+1,PrimeQ]&] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, May 26 2019 *)
%Y Cf. A120806, A120808.
%K nonn
%O 1,2
%A _Walter Kehowski_, Jul 06 2006
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