OFFSET
1,2
COMMENTS
Multiplicative because it is the inverse Moebius transform of A007913 which is multiplicative. - Christian G. Bower, May 17 2005.
LINKS
Antti Karttunen, Table of n, a(n) for n = 1..16384
FORMULA
G.f.: Sum_{k>=1} core(k)*x^k/(1-x^k). - Benoit Cloitre, Apr 21 2003
Dirichlet g.f.: zeta(2*s)*zeta(s)*zeta(s-1)/zeta(2*s-2). - R. J. Mathar, Oct 31 2011
Sum_{k=1..n} a(k) ~ Pi^4 * n^2 / 180. - Vaclav Kotesovec, Feb 01 2019
Multiplicative with a(p^e) = (p+1)*(e+1)/2 if e odd, and (p+1)*e/2 + 1 if e even. - Amiram Eldar, Sep 03 2020
MATHEMATICA
f[p_, e_] := If[OddQ[e], (p + 1)*(e + 1)/2, (p + 1)*e/2 + 1]; a[1] = 1; a[n_] := Times @@ (f @@@ FactorInteger[n]); Array[a, 100] (* Amiram Eldar, Sep 03 2020 *)
PROG
(PARI) a(n) = sumdiv(n, d, core(d) );
CROSSREFS
KEYWORD
easy,nonn,mult
AUTHOR
Benoit Cloitre, Apr 05 2002
STATUS
approved