cp's OEIS Frontend

A368336 The number of divisors of the largest term of A072873 that divides of n.

%I A368336 #7 Dec 21 2023 21:16:06
%S A368336 1,1,1,3,1,1,1,3,1,1,1,3,1,1,1,5,1,1,1,3,1,1,1,3,1,1,4,3,1,1,1,5,1,1,
%T A368336 1,3,1,1,1,3,1,1,1,3,1,1,1,5,1,1,1,3,1,4,1,3,1,1,1,3,1,1,1,7,1,1,1,3,
%U A368336 1,1,1,3,1,1,1,3,1,1,1,5,4,1,1,3,1,1,1
%N A368336 The number of divisors of the largest term of A072873 that divides of n.
%H A368336 Amiram Eldar, <a href="/A368336/b368336.txt">Table of n, a(n) for n = 1..10000</a>
%F A368336 a(n) = A000005(A327939(n)).
%F A368336 Multiplicative with a(p^e) = e - (e mod p) + 1.
%F A368336 a(n) >= 1, with equality if and only if n is in A048103.
%F A368336 a(n) <= A000005(n), with equality if and only if n is in A072873.
%F A368336 Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Product_{p prime} (1 + p/(p^p-1)) = 1.86196549645040699446... .
%t A368336 f[p_, e_] := (e - Mod[e, p] + 1); a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]
%o A368336 (PARI) a(n) = {my(f = factor(n)); prod(i = 1, #f~, f[i,2] - f[i,2]%f[i,1] + 1);}
%Y A368336 Cf. A000005, A048103, A072873, A327939, A365632, A368331, A368335.
%K A368336 nonn,easy,mult
%O A368336 1,4
%A A368336 _Amiram Eldar_, Dec 21 2023