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A127427 a(n) = v_3( (6n)! ) - v_3( (3n)! ), where v_3(N) is the 3-adic valuation A007949(N).

%I A127427 #25 Jul 19 2022 22:58:48
%S A127427 0,1,3,4,5,8,9,10,12,13,14,16,17,18,22,23,24,26,27,28,30,31,32,35,36,
%T A127427 37,39,40,41,43,44,45,48,49,50,52,53,54,56,57,58,63,64,65,67,68,69,71,
%U A127427 72,73,76,77,78,80,81,82,84,85,86,89,90,91,93,94,95,97,98,99,103,104,105,107
%N A127427 a(n) = v_3( (6n)! ) - v_3( (3n)! ), where v_3(N) is the 3-adic valuation A007949(N).
%H A127427 Sung-Hyuk Cha, <a href="http://www.wseas.us/e-library/conferences/2012/CambridgeUSA/MATHCC/MATHCC-60.pdf">On Integer Sequences Derived from Balanced k-ary Trees</a>, Applied Mathematics in Electrical and Computer Engineering, 2012. - From _N. J. A. Sloane_, Jun 12 2012
%H A127427 Sung-Hyuk Cha, <a href="http://naun.org/multimedia/UPress/ami/16-125.pdf">On Complete and Size Balanced k-ary Tree Integer Sequences</a>, International Journal of Applied Mathematics and Informatics, Issue 2, Volume 6, 2012, pp. 67-75. - From _N. J. A. Sloane_, Dec 24 2012
%F A127427 a(n) - n = a( [(n+1)/3] ).
%F A127427 a(n) = (3*n + A053735(n) - A053735(6*n))/2. - _Amiram Eldar_, Feb 21 2021
%t A127427 s[n_] := Plus @@ IntegerDigits[n, 3]; a[n_] := (3*n + s[3*n] - s[6*n])/2; Array[a, 100, 0] (* _Amiram Eldar_, Feb 21 2021 *)
%o A127427 (PARI) a(n) = valuation((6*n)!, 3) - valuation((3*n)!, 3); \\ _Michel Marcus_, Jul 29 2017
%Y A127427 Cf. A007949, A053735, A054861, A004128.
%Y A127427 Essentially partial sums of A127427.
%K A127427 nonn
%O A127427 0,3
%A A127427 _N. J. A. Sloane_, Apr 02 2007