A217984 Number of divisors of n^3 + 1 of the form a^3 + 1.

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, 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, 4, 5, 2, 4, 2, 3, 3, 5, 2, 4, 2, 3, 3, 3, 2, 6, 2, 3, 3

Offset

0,2

Links

Alois P. Heinz, Table of n, a(n) for n = 0..10000

Example

a(0) = 1: 1.
a(1) = 2: 1, 2.
a(2) = 2: 1, 9.
a(3) = 3: 1, 2, 28.
a(4) = 2: 1, 65.
a(5) = 4: 1, 2, 9, 126.
a(719) = 10: 1, 2, 9, 28, 65, 126, 217, 2745, 4914, 371694960.

Maple

with (numtheory):
q:= proc(n) local t; t:=n-1;
      is(iroot(t, 3)^3=t)
    end:
a:= n-> nops(select(q, divisors(n^3+1))):
seq (a(n), n=0..120);  # Alois P. Heinz, Nov 08 2012

Mathematica

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

Crossrefs

Cf. A001093.

Sequence in context: A111336 A083902 A205562 * A196437 A106491 A073184

Adjacent sequences: A217981 A217982 A217983 * A217985 A217986 A217987

Keyword

nonn,easy

Author

Jonathan Vos Post, Oct 16 2012

Extensions

More terms from Alois P. Heinz, Nov 08 2012

Status

approved