A167300 Totally multiplicative sequence with a(p) = 8*(p-2) for prime p.

1, 0, 8, 0, 24, 0, 40, 0, 64, 0, 72, 0, 88, 0, 192, 0, 120, 0, 136, 0, 320, 0, 168, 0, 576, 0, 512, 0, 216, 0, 232, 0, 576, 0, 960, 0, 280, 0, 704, 0, 312, 0, 328, 0, 1536, 0, 360, 0, 1600, 0, 960, 0, 408, 0, 1728, 0, 1088, 0, 456, 0, 472, 0, 2560, 0, 2112, 0

Offset

1,3

Links

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

Formula

Multiplicative with a(p^e) = (8*(p-2))^e. If n = Product p(k)^e(k) then a(n) = Product (8*(p(k)-2))^e(k).

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

a(n) = A165829(n) * A166586(n) = 8^bigomega(n) * A166586(n) = 8^A001222(n) * A166586(n).

Mathematica

a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] - 2)^fi[[All, 2]])); Table[a[n]*8^PrimeOmega[n], {n, 1, 100}] (* G. C. Greubel, Jun 07 2016 *)
f[p_, e_] := (8*(p-2))^e; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Oct 19 2023 *)

Crossrefs

Cf. A001222, A165829, A166586.

Sequence in context: A028652 A028636 A028620 * A167347 A028604 A292531

Adjacent sequences: A167297 A167298 A167299 * A167301 A167302 A167303

Keyword

nonn,easy,mult

Author

Jaroslav Krizek, Nov 01 2009

Status

approved