This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A382487 #8 Mar 29 2025 04:24:22
%S A382487 0,0,1,0,0,2,0,0,2,0,0,3,0,0,1,0,0,4,0,0,1,0,0,4,0,0,3,0,0,2,0,0,1,0,
%T A382487 0,6,0,0,1,0,0,2,0,0,2,0,0,5,0,0,1,0,0,6,0,0,1,0,0,3,0,0,2,0,0,2,0,0,
%U A382487 1,0,0,8,0,0,1,0,0,2,0,0,4,0,0,3,0,0,1
%N A382487 The number of divisors of n whose largest prime factor is 3.
%C A382487 The number of 3-smooth divisors of n that are not powers of 2.
%C A382487 The number of terms of A065119 that divide n.
%H A382487 Amiram Eldar, <a href="/A382487/b382487.txt">Table of n, a(n) for n = 1..10000</a>
%F A382487 a(n) = A072078(n) - A001511(n).
%F A382487 a(n) = A001511(n) * A007949(n).
%F A382487 a(n) = 0 if and only if n is in A001651.
%F A382487 a(n) = 1 if and only if n is in A306771.
%F A382487 Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 1.
%F A382487 In general, the asymptotic mean of the number prime(k+1)-smooth divisors of n that are not prime(k)-smooth, for k >= 1, is (1/(prime(k+1)-1)) * Product_{i=1..k} (prime(i)/(prime(i)-1)).
%F A382487 Dirichlet g.f.: (zeta(s)/(1-1/2^s))*(1/(1-1/3^s) - 1).
%t A382487 a[n_] := (IntegerExponent[n, 2] + 1) * IntegerExponent[n, 3]; Array[a, 100]
%o A382487 (PARI) a(n) = (valuation(n, 2) + 1) * valuation(n, 3);
%Y A382487 Cf. A001511, A001651, A065119, A072078, A007949, A051064, A169611, A301461, A306771.
%K A382487 nonn,easy
%O A382487 1,6
%A A382487 _Amiram Eldar_, Mar 29 2025