OFFSET
1,2
LINKS
Antti Karttunen, Table of n, a(n) for n = 1..65537
FORMULA
Multiplicative with a(2^e) = 2^(e+1)-1, a(p^e) = (p^(e+2)-1)/(p-1)/(p+1) for odd p and even e and a(p^e) = (p^(e+1)-1)/(p-1)/(p+1) for odd p and odd e.
From Amiram Eldar, Dec 15 2023: (Start)
Dirichlet g.f.: (1 + 1/2^(s-1)) * zeta(2*s-2) * zeta(s).
Sum_{k=1..n} a(k) ~ c * n^(3/2), where c = ((2+sqrt(2))/6) * zeta(3/2) = 1.4865345575818562471... . (End)
MATHEMATICA
f[2, e_] := 2^(e+1) - 1; f[p_, e_] := If[OddQ[e], (p^(e+1)-1)/(p^2-1), (p^(e+2)-1)/(p^2-1)]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Sep 13 2020 *)
PROG
(PARI) a(n) = sumdiv(n, d, issquare(d)*d + (1 - d%2)*issquare(d/2)*d) \\ Michel Marcus, Jun 17 2013
CROSSREFS
KEYWORD
mult,nonn,easy
AUTHOR
Vladeta Jovovic, Dec 04 2001
EXTENSIONS
More terms from Matthew Conroy, Jan 19 2002
STATUS
approved