A167296 Totally multiplicative sequence with a(p) = 4*(p-2) for prime p.

1, 0, 4, 0, 12, 0, 20, 0, 16, 0, 36, 0, 44, 0, 48, 0, 60, 0, 68, 0, 80, 0, 84, 0, 144, 0, 64, 0, 108, 0, 116, 0, 144, 0, 240, 0, 140, 0, 176, 0, 156, 0, 164, 0, 192, 0, 180, 0, 400, 0, 240, 0, 204, 0, 432, 0, 272, 0, 228, 0, 236, 0, 320, 0, 528, 0, 260, 0, 336

Offset: 1

Author

Jaroslav Krizek, Nov 01 2009

Keywords

• nonn
• easy
• mult

Links

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

Crossrefs

Cf. A001222, A165825, A166586.

Programs

Mathematica

a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] - 2)^fi[[All, 2]])); Table[a[n]*4^PrimeOmega[n], {n, 1, 100}] (* G. C. Greubel, Jun 06 2016 *)
f[p_, e_] := (4*(p-2))^e; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Oct 18 2023 *)

Formula

Multiplicative with a(p^e) = (4*(p-2))^e. If n = Product p(k)^e(k) then a(n) = Product (4*(p(k)-2))^e(k).

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

a(n) = A165825(n) * A166586(n) = 4^bigomega(n) * A166586(n) = 4^A001222(n) * A166586(n).