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 A072079 #16 Dec 01 2022 12:40:13
%S A072079 1,3,4,7,1,12,1,15,13,3,1,28,1,3,4,31,1,39,1,7,4,3,1,60,1,3,40,7,1,12,
%T A072079 1,63,4,3,1,91,1,3,4,15,1,12,1,7,13,3,1,124,1,3,4,7,1,120,1,15,4,3,1,
%U A072079 28,1,3,13,127,1,12,1,7,4,3,1,195,1,3,4,7,1,12,1,31,121
%N A072079 Sum of 3-smooth divisors of n.
%H A072079 Amiram Eldar, <a href="/A072079/b072079.txt">Table of n, a(n) for n = 1..10000</a>
%F A072079 a(n) = (2^(A007814(n)+1)-1)*(3^(A007949(n)+1)-1)/2.
%F A072079 a(n) = A000203(A065331(n)).
%F A072079 Multiplicative with a(2^e) = 2^(e+1)-1, a(3^e) = (3^(e+1)-1)/2, a(p^e) = 1, p>3. _Christian G. Bower_, May 20 2005
%F A072079 From _Amiram Eldar_, Dec 01 2022: (Start)
%F A072079 Dirichlet g.f.: zeta(s)*(2^s/(2^s-2))*(3^s/(3^s-3)).
%F A072079 Sum_{k=1..n} a(k) ~ c_1 * (n * log(n)^2 + c_2 * n * log(n) + c_3 * n), where c_1 = 1/(2*log(2)*log(3)) = 0.656598..., c_2 = (2*gamma - 2 + log(6)) = 0.9461907..., and c_3 = (log(6)^2 + log(2)*log(3))/6 - (log(6)-2)*(1-gamma) - 2*gamma_1 = 0.895656..., gamma is Euler's constant (A001620), and gamma_1 is the 1st Stieltjes constant (A082633). (End)
%t A072079 f[p_, e_] := If[p > 3, 1, (p^(e + 1) - 1)/(p - 1)]; a[1] = 1; a[n_] := Times @@ (f @@@ FactorInteger[n]); Array[a, 100] (* _Amiram Eldar_, Aug 29 2019 *)
%o A072079 (PARI) a(n) = (2^(valuation(n, 2)+1)-1)*(3^(valuation(n, 3)+1)-1)/2; \\ _Amiram Eldar_, Dec 01 2022
%Y A072079 Cf. A000203, A003586, A065331, A072078.
%Y A072079 Cf. A001620, A082633.
%K A072079 nonn,mult
%O A072079 1,2
%A A072079 _Reinhard Zumkeller_, Jun 13 2002