A165824 Totally multiplicative sequence with a(p) = 3.

1, 3, 3, 9, 3, 9, 3, 27, 9, 9, 3, 27, 3, 9, 9, 81, 3, 27, 3, 27, 9, 9, 3, 81, 9, 9, 27, 27, 3, 27, 3, 243, 9, 9, 9, 81, 3, 9, 9, 81, 3, 27, 3, 27, 27, 9, 3, 243, 9, 27, 9, 27, 3, 81, 9, 81, 9, 9, 3, 81, 3, 9, 27, 729, 9, 27, 3, 27, 9, 27, 3, 243, 3, 9, 27, 27

Offset: 1

Author

Jaroslav Krizek, Sep 28 2009

Keywords

• nonn
• mult

Links

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

Crossrefs

Cf. A000244, A001222, A061142, A347149, A350961 (partial sums).

Programs

Maple

A165824 := proc(n)
    3^numtheory[bigomega](n) ;
end proc:
seq(A165824(n),n=1..40) ; # R. J. Mathar, Mar 07 2022

Mathematica

3^PrimeOmega[Range[100]] (* G. C. Greubel, Apr 09 2016 *)

PARI

a(n) = 3^bigomega(n); \\ Altug Alkan, Apr 09 2016

PARI

for(n=1, 100, print1(direuler(p=2, n, 1/(1-3*X))[n], ", ")) \\ Vaclav Kotesovec, May 08 2025

Formula

a(n) = A000244(A001222(n)) = 3^bigomega(n) = 3^A001222(n).

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

Extensions

More terms from Vaclav Kotesovec, Feb 16 2022