A185021 - OEIS

%I #29 Nov 13 2018 12:50:13

%S 1,1,2,6,12,60,120,840,840,7560,15120,166320,110880,1441440,2882880,

%T 43243200,10810800,183783600,367567200,6983776800,2793510720,

%U 58663725120,117327450240,2698531355520,299836817280,7495920432000,14991840864000,404779703328000,115651343808000,3353888970432000,6707777940864000

%N 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 Although h(i) is not necessarily an integer, a(n) is.

%H Alois P. Heinz, <a href="/A185021/b185021.txt">Table of n, a(n) for n = 0..1662</a>

%H 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 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 a:= proc(n) option remember; `if`(n<1, 1, h(n)*a(n-1)) end:

%p h:= i-> i/mul((t->`if`(t::integer, t, 1))((i/2^j)), j=1..ilog2(i)):

%p seq(a(n), n=0..30);  # _Alois P. Heinz_, Oct 18 2018

%t a[n_] := a[n] = If[n<1, 1, h[n] a[n-1]];

%t h[i_] := i/Product[If[IntegerQ[#], #, 1]&[i/2^j], {j, 1, Log[2, i]}];

%t Table[a[n], {n, 0, 30}] (* _Jean-François Alcover_, Nov 13 2018, after _Alois P. Heinz_ *)

%Y Cf. A185275, A055634.

%K nonn

%O 0,3

%A _Bakir FARHI_, Jan 22 2012

%E Edited by _N. J. A. Sloane_, Apr 10 2012

%E a(0)=1 prepended by _Alois P. Heinz_, Oct 18 2018