cp's OEIS Frontend

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

%I A165824 #27 May 08 2025 07:56:15
%S A165824 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,
%T A165824 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,
%U A165824 3,81,3,9,27,729,9,27,3,27,9,27,3,243,3,9,27,27
%N A165824 Totally multiplicative sequence with a(p) = 3.
%H A165824 G. C. Greubel, <a href="/A165824/b165824.txt">Table of n, a(n) for n = 1..10000</a>
%F A165824 a(n) = A000244(A001222(n)) = 3^bigomega(n) = 3^A001222(n).
%F A165824 Dirichlet g.f.: Product_{p prime} 1 / (1 - 3 * p^(-s)). - _Ilya Gutkovskiy_, Oct 30 2019
%p A165824 A165824 := proc(n)
%p A165824     3^numtheory[bigomega](n) ;
%p A165824 end proc:
%p A165824 seq(A165824(n),n=1..40) ; # _R. J. Mathar_, Mar 07 2022
%t A165824 3^PrimeOmega[Range[100]] (* _G. C. Greubel_, Apr 09 2016 *)
%o A165824 (PARI) a(n) = 3^bigomega(n); \\ _Altug Alkan_, Apr 09 2016
%o A165824 (PARI) for(n=1, 100, print1(direuler(p=2, n, 1/(1-3*X))[n], ", ")) \\ _Vaclav Kotesovec_, May 08 2025
%Y A165824 Cf. A000244, A001222, A061142, A347149, A350961 (partial sums).
%K A165824 nonn,mult
%O A165824 1,2
%A A165824 _Jaroslav Krizek_, Sep 28 2009
%E A165824 More terms from _Vaclav Kotesovec_, Feb 16 2022