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A377519 The number of divisors of n that are terms in A207481.

%I A377519 #6 Oct 31 2024 01:11:41
%S A377519 1,2,2,3,2,4,2,3,3,4,2,6,2,4,4,3,2,6,2,6,4,4,2,6,3,4,4,6,2,8,2,3,4,4,
%T A377519 4,9,2,4,4,6,2,8,2,6,6,4,2,6,3,6,4,6,2,8,4,6,4,4,2,12,2,4,6,3,4,8,2,6,
%U A377519 4,8,2,9,2,4,6,6,4,8,2,6,4,4,2,12,4,4,4
%N A377519 The number of divisors of n that are terms in A207481.
%C A377519 The sum of these divisors is A377520(n), and the largest of them is A377518(n).
%H A377519 Amiram Eldar, <a href="/A377519/b377519.txt">Table of n, a(n) for n = 1..10000</a>
%F A377519 a(n) = A000005(A377518(n)).
%F A377519 Multiplicative with a(p^e) = min(p, e) + 1.
%F A377519 Dirichlet g.f.: zeta(s)^2 * Product_{p prime} (1 - 1/p^((p+1)*s)).
%t A377519 f[p_, e_] := Min[p, e] + 1; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]
%o A377519 (PARI) a(n) = {my(f = factor(n)); prod(i = 1, #f~, min(f[i,1], f[i,2]) + 1);}
%Y A377519 Cf. A000005, A013661, A207481, A377516, A377518, A377520.
%K A377519 nonn,easy,mult
%O A377519 1,2
%A A377519 _Amiram Eldar_, Oct 30 2024