cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

User: Bakir FARHI

Bakir FARHI's wiki page.

Bakir FARHI has authored 2 sequences.

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.

Original entry on oeis.org

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

Views

Author

Bakir FARHI, Jan 22 2012

Keywords

Comments

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

Links

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

A185275 Products of the first terms of the arithmetic sequence f(n) defined by f(2^k l) = l^{1 - k} (for k a nonnegative integer and l a positive odd integer).

Original entry on oeis.org

1, 1, 3, 3, 15, 15, 105, 105, 945, 945, 10395, 3465, 45045, 45045, 675675, 675675, 11486475, 11486475, 218243025, 43648605, 916620705, 916620705, 21082276215, 2342475135, 58561878375, 58561878375, 1581170716125, 225881530875, 6550564395375, 6550564395375
Offset: 0

Views

Author

Bakir FARHI, Jan 21 2012

Keywords

Comments

Note that f(n) is not always an integer (for example f(12) = 1/3) but Farhi showed in his paper that the product Product_{i = 1..n} f(i) is always an integer.

Links

Crossrefs

Cf. A185021, A055634.

Formula

G.f.: G(0)/x -1/x, where G(k)= 1 + x*(2*k+1)/(1 - x/(x + 1/G(k+1))); (continued fraction). - Sergei N. Gladkovskii, Jun 07 2013

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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