A138011 a(n) = number of positive divisors, k, of n where d(k) divides d(n). (d(m) = number of positive divisors of m, A000005).

1, 2, 2, 2, 2, 4, 2, 3, 2, 4, 2, 5, 2, 4, 4, 2, 2, 5, 2, 5, 4, 4, 2, 6, 2, 4, 3, 5, 2, 8, 2, 4, 4, 4, 4, 4, 2, 4, 4, 6, 2, 8, 2, 5, 5, 4, 2, 5, 2, 5, 4, 5, 2, 6, 4, 6, 4, 4, 2, 11, 2, 4, 5, 2, 4, 8, 2, 5, 4, 8, 2, 10, 2, 4, 5, 5, 4, 8, 2, 5, 2, 4, 2, 11, 4, 4, 4, 6, 2, 11, 4, 5, 4, 4, 4, 9, 2, 5, 5, 4

Offset: 1

Author

Leroy Quet, Feb 27 2008

Keywords

• nonn

Examples

			12 has 6 divisors (1,2,3,4,6,12). The number of divisors of each of these divisors of 12 form the sequence (1,2,2,3,4,6). Of these, five divide d(12)=6: 1,2,2,3,6. So a(12) = 5.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000005, A138010, A138012.

Programs

Mathematica

Table[Length[Select[Divisors[n], Mod[Length[Divisors[n]], Length[Divisors[ # ]]] == 0 &]], {n, 1, 100}] (* Stefan Steinerberger, Feb 29 2008 *)

PARI

A138011(n) = sumdiv(n,d,if(!(numdiv(n)%numdiv(d)), 1, 0)); \\ Antti Karttunen, May 25 2017

Python

from sympy import divisors, divisor_count
def a(n): return sum([1*(divisor_count(n)%divisor_count(d)==0) for d in divisors(n)]) # Indranil Ghosh, May 25 2017

Extensions

More terms from Stefan Steinerberger, Feb 29 2008