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

1,3

Links

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

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).

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 *)

Crossrefs

Cf. A001222, A165825, A166586.

Sequence in context: A260490 A349712 A349711 * A147607 A174087 A072194

Adjacent sequences: A167293 A167294 A167295 * A167297 A167298 A167299

Keyword

nonn,easy,mult

Author

Jaroslav Krizek, Nov 01 2009

Status

approved