A167314 Totally multiplicative sequence with a(p) = 4*(p-3) for prime p.

1, -4, 0, 16, 8, 0, 16, -64, 0, -32, 32, 0, 40, -64, 0, 256, 56, 0, 64, 128, 0, -128, 80, 0, 64, -160, 0, 256, 104, 0, 112, -1024, 0, -224, 128, 0, 136, -256, 0, -512, 152, 0, 160, 512, 0, -320, 176, 0, 256, -256, 0, 640, 200, 0, 256, -1024, 0, -416, 224, 0, 232

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, A165825, A166589.

Programs

Mathematica

a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] - 3)^fi[[All, 2]])); Table[a[n]*4^PrimeOmega[n], {n, 1, 100}] (* G. C. Greubel, Jun 08 2016 *)
f[p_, e_] := (4*(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) = (4*(p-3))^e. If n = Product p(k)^e(k) then a(n) = Product (4*(p(k)-3))^e(k).

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

a(n) = A165825(n) * A166589(n) = 4^bigomega(n) * A166589(n) = 4^A001222(n) * A166589(n).