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

1,2

Links

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

Example

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.

Mathematica

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

Prog

(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

Crossrefs

Cf. A000005, A138010, A138012.

Sequence in context: A322483 A061389 A366763 * A036555 A046927 A366563

Adjacent sequences: A138008 A138009 A138010 * A138012 A138013 A138014

Keyword

nonn

Author

Leroy Quet, Feb 27 2008

Extensions

More terms from Stefan Steinerberger, Feb 29 2008

Status

approved