A129294 Number of divisors of n^3 - 1 that are not greater than n.

1, 2, 2, 3, 2, 4, 2, 5, 3, 5, 2, 7, 2, 4, 7, 5, 3, 6, 2, 6, 6, 6, 2, 13, 4, 4, 4, 8, 4, 10, 3, 6, 5, 6, 5, 14, 2, 6, 5, 8, 3, 10, 3, 8, 10, 5, 3, 16, 3, 9, 5, 9, 2, 11, 5, 8, 7, 4, 3, 20, 2, 5, 9, 11, 4, 18, 4, 6, 5, 8, 3, 14, 5, 4, 8, 6, 4, 17, 2, 21, 5, 6, 3, 16, 6, 10, 8, 8, 2, 14, 5, 9, 7, 6, 5, 16

Offset: 2

Author

Reinhard Zumkeller, Apr 09 2007

Keywords

• nonn

Comments

a(n) = #{d: d<=n and A068601(n) mod d = 0};

a(n)>1 for n>2, see A129295 for m such that a(m)=2: a(A129295(n))=2.

Examples

			a(100) = #{1,3,7,9,11,13,21,27,33,37,39,63,77,91,99} = 15.
		

Links

• R. Zumkeller, Table of n, a(n) for n = 2..1000

Crossrefs

Cf. A129292, A129296.

Programs

Mathematica

Table[Count[Divisors[n^3-1],?(#<n+1&)],{n,2,100}] (* _Harvey P. Dale, Sep 27 2018 *)

PARI

a(n) = sumdiv(n^3-1, d, d <= n); \\ Michel Marcus, Aug 01 2018

Extensions

a(1)=1 removed by Michel Marcus, Aug 01 2018