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.

1, 1, 2, 6, 12, 60, 120, 840, 840, 7560, 15120, 166320, 110880, 1441440, 2882880, 43243200, 10810800, 183783600, 367567200, 6983776800, 2793510720, 58663725120, 117327450240, 2698531355520, 299836817280, 7495920432000, 14991840864000, 404779703328000, 115651343808000, 3353888970432000, 6707777940864000

Offset: 0

Author

Bakir FARHI, Jan 22 2012

Keywords

• nonn

Comments

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

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1662
• B. Farhi, A study of a curious arithmetic function, arXiv:1004.2269 [math.NT], April 13 2010.
• Bakir Farhi, A Study of a Curious Arithmetic Function, Journal of Integer Sequences, Vol. 15 (2012), #12.3.1.

Crossrefs

Cf. A185275, A055634.

Programs

Maple

a:= proc(n) option remember; `if`(n<1, 1, h(n)*a(n-1)) end:
h:= i-> i/mul((t->`if`(t::integer, t, 1))((i/2^j)), j=1..ilog2(i)):
seq(a(n), n=0..30);  # Alois P. Heinz, Oct 18 2018

Mathematica

a[n_] := a[n] = If[n<1, 1, h[n] a[n-1]];
h[i_] := i/Product[If[IntegerQ[#], #, 1]&[i/2^j], {j, 1, Log[2, i]}];
Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Nov 13 2018, after Alois P. Heinz *)

Extensions

Edited by N. J. A. Sloane, Apr 10 2012

a(0)=1 prepended by Alois P. Heinz, Oct 18 2018