cp's OEIS Frontend

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).

%I A138011 #17 Jun 02 2025 00:32:44
%S A138011 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,
%T A138011 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,
%U A138011 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
%N 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).
%H A138011 Antti Karttunen, <a href="/A138011/b138011.txt">Table of n, a(n) for n = 1..10000</a>
%e A138011 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.
%t A138011 Table[Length[Select[Divisors[n], Mod[Length[Divisors[n]], Length[Divisors[ # ]]] == 0 &]], {n, 1, 100}] (* _Stefan Steinerberger_, Feb 29 2008 *)
%o A138011 (PARI) A138011(n) = sumdiv(n,d,if(!(numdiv(n)%numdiv(d)), 1, 0)); \\ _Antti Karttunen_, May 25 2017
%o A138011 (Python)
%o A138011 from sympy import divisors, divisor_count
%o A138011 def a(n): return sum([1*(divisor_count(n)%divisor_count(d)==0) for d in divisors(n)]) # _Indranil Ghosh_, May 25 2017
%Y A138011 Cf. A000005, A138010, A138012.
%K A138011 nonn
%O A138011 1,2
%A A138011 _Leroy Quet_, Feb 27 2008
%E A138011 More terms from _Stefan Steinerberger_, Feb 29 2008