A167313 Totally multiplicative sequence with a(p) = 3*(p-3) for prime p.

1, -3, 0, 9, 6, 0, 12, -27, 0, -18, 24, 0, 30, -36, 0, 81, 42, 0, 48, 54, 0, -72, 60, 0, 36, -90, 0, 108, 78, 0, 84, -243, 0, -126, 72, 0, 102, -144, 0, -162, 114, 0, 120, 216, 0, -180, 132, 0, 144, -108, 0, 270, 150, 0, 144, -324, 0, -234, 168, 0, 174, -252, 0

Offset: 1

Author

Jaroslav Krizek, Nov 01 2009

Keywords

• sign
• easy
• mult

Links

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

Crossrefs

Cf. A001222, A165824, A166589.

Programs

Mathematica

a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] - 3)^fi[[All, 2]])); Table[a[n]*3^PrimeOmega[n], {n, 1, 100}] (* G. C. Greubel, Jun 08 2016 *)
f[p_, e_] := (3*(p-3))^e; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Oct 21 2023 *)

Formula

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

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

a(n) = A165824(n) * A166589(n) = 3^bigomega(n) * A166589(n) = 3^A001222(n) * A166589(n).