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A185021 a(n) = h(1)*h(2)*...*h(n), where h(i) = i/[g(i/2)*g(i/4)*g(i/8)*...] and g(x) = x if x is an integer and g(x) = 1 otherwise.

%I A185021 #29 Nov 13 2018 12:50:13
%S A185021 1,1,2,6,12,60,120,840,840,7560,15120,166320,110880,1441440,2882880,
%T A185021 43243200,10810800,183783600,367567200,6983776800,2793510720,
%U A185021 58663725120,117327450240,2698531355520,299836817280,7495920432000,14991840864000,404779703328000,115651343808000,3353888970432000,6707777940864000
%N A185021 a(n) = h(1)*h(2)*...*h(n), where h(i) = i/[g(i/2)*g(i/4)*g(i/8)*...] and g(x) = x if x is an integer and g(x) = 1 otherwise.
%C A185021 Although h(i) is not necessarily an integer, a(n) is.
%H A185021 Alois P. Heinz, <a href="/A185021/b185021.txt">Table of n, a(n) for n = 0..1662</a>
%H A185021 B. Farhi, <a href="https://arxiv.org/abs/1004.2269">A study of a curious arithmetic function</a>, arXiv:1004.2269 [math.NT], April 13 2010.
%H A185021 Bakir Farhi, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL15/Farhi/farhi3.html">A Study of a Curious Arithmetic Function</a>, Journal of Integer Sequences, Vol. 15 (2012), #12.3.1.
%p A185021 a:= proc(n) option remember; `if`(n<1, 1, h(n)*a(n-1)) end:
%p A185021 h:= i-> i/mul((t->`if`(t::integer, t, 1))((i/2^j)), j=1..ilog2(i)):
%p A185021 seq(a(n), n=0..30);  # _Alois P. Heinz_, Oct 18 2018
%t A185021 a[n_] := a[n] = If[n<1, 1, h[n] a[n-1]];
%t A185021 h[i_] := i/Product[If[IntegerQ[#], #, 1]&[i/2^j], {j, 1, Log[2, i]}];
%t A185021 Table[a[n], {n, 0, 30}] (* _Jean-François Alcover_, Nov 13 2018, after _Alois P. Heinz_ *)
%Y A185021 Cf. A185275, A055634.
%K A185021 nonn
%O A185021 0,3
%A A185021 _Bakir FARHI_, Jan 22 2012
%E A185021 Edited by _N. J. A. Sloane_, Apr 10 2012
%E A185021 a(0)=1 prepended by _Alois P. Heinz_, Oct 18 2018