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

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, A165827, A166586.

Programs

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 *)

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).