A365632 - OEIS

%I #13 Sep 20 2023 05:41:08

%S 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 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 1,1,1,2,1,1,1,2,1,1,1,3,2,1,1,2,1,1,1

%N The number of divisors of n that are terms of A072873.

%C The sum of these divisors is A365633(n) and the largest of them is A327939(n).

%H Amiram Eldar, <a href="/A365632/b365632.txt">Table of n, a(n) for n = 1..10000</a>

%F Multiplicative with a(p^e) = 1 + floor(e/p).

%F Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Product_{p prime} p^p/(p^p-1) = 1.3850602852... .

%t f[p_, e_] := 1 + Floor[e/p]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]

%o (PARI) a(n) = {my(f = factor(n)); prod(i = 1, #f~, 1 + f[i,2]\f[i,1]);}

%Y Cf. A072873, A327939, A365633, A365634.

%K nonn,easy,mult

%O 1,4

%A _Amiram Eldar_, Sep 14 2023

%E Data corrected by _Amiram Eldar_, Sep 20 2023