A167295 Totally multiplicative sequence with a(p) = 3*(p-2) for prime p.

1, 0, 3, 0, 9, 0, 15, 0, 9, 0, 27, 0, 33, 0, 27, 0, 45, 0, 51, 0, 45, 0, 63, 0, 81, 0, 27, 0, 81, 0, 87, 0, 81, 0, 135, 0, 105, 0, 99, 0, 117, 0, 123, 0, 81, 0, 135, 0, 225, 0, 135, 0, 153, 0, 243, 0, 153, 0, 171, 0, 177, 0, 135, 0, 297, 0, 195, 0, 189, 0, 207

Offset

1,3

Links

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

Formula

Multiplicative with a(p^e) = (3*(p-2))^e. If n = Product p(k)^e(k) then a(n) = Product (3*(p(k)-2))^e(k).

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

a(n) = A165824(n) * A166586(n) = 3^bigomega(n) * A166586(n) = 3^A001222(n) * A166586(n).

Mathematica

a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] - 2)^fi[[All, 2]])); Table[a[n]*3^PrimeOmega[n], {n, 1, 100}](* G. C. Greubel, Jun 05 2016 *)
f[p_, e_] := (3*(p-2))^e; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Oct 19 2023 *)

Crossrefs

Cf. A001222, A165824, A166586.

Sequence in context: A269557 A201581 A164597 * A079442 A254006 A321329

Adjacent sequences: A167292 A167293 A167294 * A167296 A167297 A167298

Keyword

nonn,easy,mult

Author

Jaroslav Krizek, Nov 01 2009

Status

approved