OFFSET
1,2
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
FORMULA
a(n) = n/A055229(n)^3 = n/g^3=n/ggg and n=(LL)*(ggg)*f=L^2*g^3*f=LL*a(n)^3*f, so n=L^2*(g*3)*f, where L=A000188(n)/A055229(n), f=A055231(n), g=A055231(n).
Multiplicative with a(p^e)=p^e for even e, a(p)=p, a(p^e)=p^(e-3) for odd e>1. - Vladeta Jovovic, Apr 30 2002
Sum_{k=1..n} a(k) ~ c * n^2, where c = (Pi^2/12) * Product_{p prime} (1 - 1/p^2 - 1/p^3 + 1/p^4 + 1/p^6 - 1/p^7) = 0.4462648652... . - Amiram Eldar, Nov 13 2022
MATHEMATICA
f[p_, e_] := If[EvenQ[e], p^e, If[e == 1, p, p^(e - 3)]]; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Sep 06 2020 *)
CROSSREFS
KEYWORD
nonn,mult
AUTHOR
Labos Elemer, Aug 02 2000
STATUS
approved