cp's OEIS Frontend

A365634 The number of divisors of n that are terms of A048102.

%I A365634 #13 Sep 05 2024 16:23:07
%S A365634 1,1,1,2,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,2,1,1,1,1,1,1,2,2,1,1,1,1,1,1,
%T A365634 1,2,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,2,1,2,1,1,1,1,1,2,1,1,1,1,1,1,1,2,
%U A365634 1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,2,1,1,1
%N A365634 The number of divisors of n that are terms of A048102.
%H A365634 Amiram Eldar, <a href="/A365634/b365634.txt">Table of n, a(n) for n = 1..10000</a>
%F A365634 Multiplicative with a(p^e) = 1 + [e = p], where [] is the Iverson bracket.
%F A365634 Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Product_{p prime} (1 + (p-1)/p^(p+1)) = 1.153074089009... .
%t A365634 f[p_, e_] := If[e == p, 2, 1]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]
%o A365634 (PARI) a(n) = {my(f = factor(n)); prod(i = 1, #f~, if(f[i,2] == f[i,1], 2, 1));}
%Y A365634 Cf. A048102, A365632, A365635.
%K A365634 nonn,easy,mult
%O A365634 1,4
%A A365634 _Amiram Eldar_, Sep 14 2023