cp's OEIS Frontend

A365632 The number of divisors of n that are terms of A072873.

%I A365632 #13 Sep 20 2023 05:41:08
%S A365632 1,1,1,2,1,1,1,2,1,1,1,2,1,1,1,3,1,1,1,2,1,1,1,2,1,1,2,2,1,1,1,3,1,1,
%T A365632 1,2,1,1,1,2,1,1,1,2,1,1,1,3,1,1,1,2,1,2,1,2,1,1,1,2,1,1,1,4,1,1,1,2,
%U A365632 1,1,1,2,1,1,1,2,1,1,1,3,2,1,1,2,1,1,1
%N A365632 The number of divisors of n that are terms of A072873.
%C A365632 The sum of these divisors is A365633(n) and the largest of them is A327939(n).
%H A365632 Amiram Eldar, <a href="/A365632/b365632.txt">Table of n, a(n) for n = 1..10000</a>
%F A365632 Multiplicative with a(p^e) = 1 + floor(e/p).
%F A365632 Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Product_{p prime} p^p/(p^p-1) = 1.3850602852... .
%t A365632 f[p_, e_] := 1 + Floor[e/p]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]
%o A365632 (PARI) a(n) = {my(f = factor(n)); prod(i = 1, #f~, 1 + f[i,2]\f[i,1]);}
%Y A365632 Cf. A072873, A327939, A365633, A365634.
%K A365632 nonn,easy,mult
%O A365632 1,4
%A A365632 _Amiram Eldar_, Sep 14 2023
%E A365632 Data corrected by _Amiram Eldar_, Sep 20 2023