A167298 Totally multiplicative sequence with a(p) = 6*(p-2) for prime p.

1, 0, 6, 0, 18, 0, 30, 0, 36, 0, 54, 0, 66, 0, 108, 0, 90, 0, 102, 0, 180, 0, 126, 0, 324, 0, 216, 0, 162, 0, 174, 0, 324, 0, 540, 0, 210, 0, 396, 0, 234, 0, 246, 0, 648, 0, 270, 0, 900, 0, 540, 0, 306, 0, 972, 0, 612, 0, 342, 0, 354, 0, 1080, 0, 1188, 0, 390

Offset

1,3

Links

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

Formula

Multiplicative with a(p^e) = (6*(p-2))^e. If n = Product p(k)^e(k) then a(n) = Product (6*(p(k)-2))^e(k).

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

a(n) = A165827(n) * A166586(n) = 6^bigomega(n) * A166586(n) = 6^A001222(n) * A166586(n).

Mathematica

a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] - 2)^fi[[All, 2]])); Table[a[n]*6^PrimeOmega[n], {n, 1, 100}] (* G. C. Greubel, Jun 07 2016 *)
f[p_, e_] := (6*(p-2))^e; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Oct 28 2023 *)

Crossrefs

Cf. A001222, A165827, A166586.

Sequence in context: A057401 A308236 A019134 * A242838 A304878 A167356

Adjacent sequences: A167295 A167296 A167297 * A167299 A167300 A167301

Keyword

nonn,easy,mult

Author

Jaroslav Krizek, Nov 01 2009

Status

approved