A167339 Totally multiplicative sequence with a(p) = p*(p-2) = p^2-2p for prime p.

1, 0, 3, 0, 15, 0, 35, 0, 9, 0, 99, 0, 143, 0, 45, 0, 255, 0, 323, 0, 105, 0, 483, 0, 225, 0, 27, 0, 783, 0, 899, 0, 297, 0, 525, 0, 1295, 0, 429, 0, 1599, 0, 1763, 0, 135, 0, 2115, 0, 1225, 0

Offset: 1

Author

Jaroslav Krizek, Nov 01 2009

Keywords

• nonn
• mult

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A166586.

Programs

Mathematica

a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] - 2)^fi[[All, 2]])); Table[a[n]*n, {n, 1, 100}] (* G. C. Greubel, Jun 08 2016 *)

Formula

Multiplicative with a(p^e) = (p*(p-2))^e. If n = Product p(k)^e(k) then a(n) = Product (p(k)*(p(k)-2))^e(k).

a(2k) = 0 for k >= 1.

a(n) = n * A166586(n).

Sum_{k=1..n} a(k) ~ c * n^3, where c = (2/Pi^2) / Product_{p prime} (1 + 1/p^2 + 2/p^3) = 0.1016391193... . - Amiram Eldar, Dec 15 2022