A217984 - OEIS

%I #24 Nov 15 2012 15:09:11

%S 1,2,2,3,2,4,2,3,3,3,2,4,2,3,3,3,2,5,2,4,3,3,2,4,2,3,4,4,2,4,2,4,3,3,

%T 2,4,2,3,3,3,2,5,2,3,3,3,2,6,2,4,3,3,2,4,2,4,3,3,2,6,2,4,3,3,3,4,2,3,

%U 4,5,2,4,2,3,3,5,2,4,2,3,3,3,2,6,2,3,3

%N Number of divisors of n^3 + 1 of the form a^3 + 1.

%H Alois P. Heinz, <a href="/A217984/b217984.txt">Table of n, a(n) for n = 0..10000</a>

%e a(0) = 1: 1.

%e a(1) = 2: 1, 2.

%e a(2) = 2: 1, 9.

%e a(3) = 3: 1, 2, 28.

%e a(4) = 2: 1, 65.

%e a(5) = 4: 1, 2, 9, 126.

%e a(719) = 10: 1, 2, 9, 28, 65, 126, 217, 2745, 4914, 371694960.

%p with (numtheory):

%p q:= proc(n) local t; t:=n-1;

%p       is(iroot(t, 3)^3=t)

%p     end:

%p a:= n-> nops(select(q, divisors(n^3+1))):

%p seq (a(n), n=0..120);  # _Alois P. Heinz_, Nov 08 2012

%t Table[Count[Divisors[n^3+1],_?(IntegerQ[(#-1)^(1/3)]&)],{n,0,90}] (* _Harvey P. Dale_, Nov 15 2012 *)

%Y Cf. A001093.

%K nonn,easy

%O 0,2

%A _Jonathan Vos Post_, Oct 16 2012

%E More terms from _Alois P. Heinz_, Nov 08 2012