A167341 Totally multiplicative sequence with a(p) = p*(p-3) = p^2-3p for prime p.

1, -2, 0, 4, 10, 0, 28, -8, 0, -20, 88, 0, 130, -56, 0, 16, 238, 0, 304, 40, 0, -176, 460, 0, 100, -260, 0, 112, 754, 0, 868, -32, 0, -476, 280, 0, 1258, -608, 0, -80, 1558, 0, 1720, 352, 0, -920, 2068, 0, 784, -200

Offset: 1

Author

Jaroslav Krizek, Nov 01 2009

Keywords

• sign
• mult

Links

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

Crossrefs

Cf. A166589.

Programs

Mathematica

a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] - 3)^fi[[All, 2]])); Table[a[n]*n, {n, 1, 100}] (* G. C. Greubel, Jun 10 2016 *)

Formula

Multiplicative with a(p^e) = (p*(p-3))^e. If n = Product p(k)^e(k) then a(n) = Product (p(k)*(p(k)-3))^e(k).

a(3k) = 0 for k >= 1.

a(n) = n * A166589(n).

Sum_{k=1..n} a(k) ~ c * n^3, where c = (2/Pi^2) / Product_{p prime} (1 + 2/p^2 + 3/p^3) = 0.06544931251... . - Amiram Eldar, Dec 15 2022