cp's OEIS Frontend

A183039 a(n) = A051064(n)*3^A051064(n) where A051064(n) equals the 3-adic valuation of 3n.

%I A183039 #11 Jul 02 2024 14:43:35
%S A183039 3,3,18,3,3,18,3,3,81,3,3,18,3,3,18,3,3,81,3,3,18,3,3,18,3,3,324,3,3,
%T A183039 18,3,3,18,3,3,81,3,3,18,3,3,18,3,3,81,3,3,18,3,3,18,3,3,324,3,3,18,3,
%U A183039 3,18,3,3,81,3,3,18,3,3,18,3,3,81,3,3,18,3,3,18,3,3,1215,3,3,18,3,3,18,3,3,81
%N A183039 a(n) = A051064(n)*3^A051064(n) where A051064(n) equals the 3-adic valuation of 3n.
%C A183039 3^A051064(n) exactly divides 3n.
%H A183039 Antti Karttunen, <a href="/A183039/b183039.txt">Table of n, a(n) for n = 1..59049</a>
%F A183039 Logarithmic derivative of A183038.
%e A183039 L.g.f.: A(x) = 3*x + 3*x^2/2 + 18*x^3/3 + 3*x^4/4 + 3*x^5/5 + 18*x^6/6 + 3*x^7/7 + 3*x^8/8 + 81*x^9/9 + 3*x^10/10 + 3*x^11/11 + 18*x^12/12 +...
%e A183039 The g.f. of A183038 begins:
%e A183039 exp(A(x)) = 1 + 3*x + 6*x^2 + 15*x^3 + 30*x^4 + 51*x^5 + 93*x^6 +...
%o A183039 (PARI) {a(n)=valuation(3*n,3)*3^valuation(3*n,3)}
%Y A183039 Cf. A183038, A183037.
%K A183039 nonn
%O A183039 1,1
%A A183039 _Paul D. Hanna_, Dec 19 2010