OFFSET
1,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..1000
FORMULA
Multiplicative with a(p^e) = ((p+1)*(p-3))^e. If n = Product p(k)^e(k) then a(n) = Product ((p(k)+1)*(p(k)-3))^e(k).
a(3k) = 0 for k >= 1.
Sum_{k=1..n} a(k) ~ c * n^3, where c = (2/Pi^2) / Product_{p prime} (1 + 1/p^2 + 5/p^3 + 3/p^4) = 0.0629795941629... . - Amiram Eldar, Dec 15 2022
MATHEMATICA
a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] - 3)^fi[[All, 2]])); b[1] = 1; b[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] + 1)^fi[[All, 2]])); Table[a[n]*b[n], {n, 1, 100}] (* G. C. Greubel, Jun 11 2016 *)
CROSSREFS
KEYWORD
sign,mult
AUTHOR
Jaroslav Krizek, Nov 01 2009
STATUS
approved