A129292 Number of divisors of n^4 - 1 that are not greater than n.

1, 1, 2, 2, 4, 2, 6, 4, 5, 3, 8, 3, 10, 4, 6, 4, 12, 4, 13, 4, 11, 6, 14, 3, 10, 6, 12, 6, 17, 3, 16, 7, 10, 9, 13, 4, 18, 7, 11, 4, 22, 3, 26, 8, 9, 7, 23, 5, 18, 7, 13, 6, 25, 4, 24, 8, 21, 6, 18, 3, 18, 10, 12, 14, 16, 4, 26, 8, 17, 7, 31, 5, 30, 6, 11, 13, 26, 7, 25, 6, 16, 10, 35, 4, 18, 11

Offset: 1

Author

Reinhard Zumkeller, Apr 09 2007

Keywords

• nonn

Comments

a(n) = #{d: d<=n and A123865(n) mod d = 0};

a(n)>1 for n>2, see A129293 for m such that a(m)=2: a(A129293(n))=2.

Examples

			a(100) = #{1,3,9,11,33,73,99} = 7.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A129294, A129296.

Programs

Maple

f:= n -> nops(select(`<=`,numtheory:-divisors(n^4-1),n)):
1,seq(f(n), n=2..100); # Robert Israel, Sep 21 2014

Mathematica

Table[Count[Divisors[n^4-1],?(#<=n&)],{n,90}] (* _Harvey P. Dale, Aug 13 2014 *)

PARI

a(n) = if (n==1, 1, sumdiv(n^4-1, d, d <= n)); \\ Michel Marcus, Sep 21 2014