cp's OEIS Frontend

A377516 The number of divisors of n that are terms in A276078.

%I A377516 #7 Oct 31 2024 01:11:13
%S A377516 1,2,2,2,2,4,2,2,3,4,2,4,2,4,4,2,2,6,2,4,4,4,2,4,3,4,3,4,2,8,2,2,4,4,
%T A377516 4,6,2,4,4,4,2,8,2,4,6,4,2,4,3,6,4,4,2,6,4,4,4,4,2,8,2,4,6,2,4,8,2,4,
%U A377516 4,8,2,6,2,4,6,4,4,8,2,4,3,4,2,8,4,4,4
%N A377516 The number of divisors of n that are terms in A276078.
%C A377516 The sum of these divisors is A377517(n), and the largest of them is A377515(n).
%H A377516 Amiram Eldar, <a href="/A377516/b377516.txt">Table of n, a(n) for n = 1..10000</a>
%F A377516 a(n) = A000005(A377515(n)).
%F A377516 Multiplicative with a(p^e) = min(pi(p), e) + 1, where pi(n) = A000720(n).
%F A377516 Dirichlet g.f.: zeta(s)^2 * Product_{p prime} (1 - 1/p^((pi(p)+1)*s)).
%t A377516 f[p_, e_] := Min[PrimePi[p], e] + 1; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]
%o A377516 (PARI) a(n) = {my(f = factor(n)); prod(i = 1, #f~, min(primepi(f[i,1]), f[i,2]) + 1);}
%Y A377516 Cf. A000005, A000720, A013661, A276078, A377515, A377517, A377519.
%K A377516 nonn,easy,mult
%O A377516 1,2
%A A377516 _Amiram Eldar_, Oct 30 2024