A161887 A product of quotients of factorials.

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

Offset: 1

Author

Peter Luschny, Jun 21 2009

Keywords

• easy
• nonn

Comments

Definition: Let b(n,k) = floor(n/2^k)! and m = log[2](n) then c(n) = product_{k=1..m} b(n,k) / b(n,k+1)^2.

a(n) is the sequence derived from c(n) by eliminating duplicates and sorting the values.

a(1) through a(19) are highly composite numbers (A002182).

The number of divisors of a(1) through a(28) are number of divisors of highly composite numbers (A002183).

A055773(floor(n/2)) is a divisor of a(n), a(n)/A055773(floor(n/2)) after eliminating duplicates and sorting starts 1,4,24,216,1440,2160,..

Links

• Amiram Eldar, Table of n, a(n) for n = 1..1669

Crossrefs

Cf. A002182, A002183.

Programs

Maple

a := proc(n) local m,k; m := nops(convert(n,base,2));
mul(iquo(n,2^k)!/iquo(n,2^(k+1))!^2,k=1..m-1) end:
seq(a(i),i=1..50): A:=sort(convert({%},list));

Mathematica

b[n_, k_] := Floor[n/2^k]!; c[n_] := Product[b[n, k]/b[n, k+1]^2, {k, 1, Log[2, n]}]; A = Array[c, 50] // DeleteDuplicates // Sort (* Jean-François Alcover, Jun 17 2019 *)