A166624 Totally multiplicative sequence with a(p) = 3p for prime p.

1, 6, 9, 36, 15, 54, 21, 216, 81, 90, 33, 324, 39, 126, 135, 1296, 51, 486, 57, 540, 189, 198, 69, 1944, 225, 234, 729, 756, 87, 810, 93, 7776, 297, 306, 315, 2916, 111, 342, 351, 3240, 123, 1134, 129, 1188, 1215, 414, 141, 11664, 441, 1350

Offset: 1

Author

Jaroslav Krizek, Oct 18 2009

Keywords

• nonn
• mult

Links

• G. C. Greubel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001222, A165824.

Programs

Mathematica

Table[n*3^PrimeOmega[n], {n, 1, 100}] (* G. C. Greubel, May 19 2016 *)

Formula

Multiplicative with a(p^e) = (3p)^e.

If n = Product p(k)^e(k) then a(n) = Product (3*p(k))^e(k).

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

Dirichlet g.f.: Product_{p prime} 1 / (1 - 3 * p^(1 - s)). - Ilya Gutkovskiy, Oct 30 2019