OFFSET
1,2
LINKS
Seiichi Manyama, Table of n, a(n) for n = 1..10000
FORMULA
G.f.: Sum_{k>0} x^k*(1+x^k)^2*(1+x^(2*k))/(1-x^(3*k))^2.
G.f.: Sum_{k>=1} k*x^k*(1 + x^k)/(1 - x^(3*k)). - Ilya Gutkovskiy, Sep 13 2019
From R. J. Mathar, May 25 2020: (Start)
From Amiram Eldar, Oct 30 2022: (Start)
Multiplicative with a(3^e) = 3^e and a(p^e) = (p^(e+1)-1)/(p-1) if p != 3.
Sum_{k=1..n} a(k) ~ c * n^2, where c = 2*Pi^2/27 = 0.731081... (A346933). (End)
Dirichlet g.f.: zeta(s)*zeta(s-1)*(1-1/3^s). - Amiram Eldar, Dec 30 2022
MATHEMATICA
f[p_, e_] := If[p == 3, 3^e, (p^(e+1)-1)/(p-1)]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Oct 30 2022 *)
PROG
(PARI) for(n=1, 70, d=divisors(n); s=0; for(j=1, matsize(d)[2], if((n/d[j])%3>0, s=s+d[j])); print1(s, ", "))
(PARI) a(n)=sumdiv(n, d, if((n/d)%3, 1, 0)*d)
CROSSREFS
KEYWORD
mult,easy,nonn
AUTHOR
Vladeta Jovovic, Dec 18 2002
EXTENSIONS
Extended by Klaus Brockhaus and Benoit Cloitre, Dec 20 2002
STATUS
approved