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

1,2

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

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 *)

Crossrefs

Cf. A002182, A002183.

Sequence in context: A096123 A081125 A138570 * A139315 A014767 A002319

Adjacent sequences: A161884 A161885 A161886 * A161888 A161889 A161890

Keyword

easy,nonn

Author

Peter Luschny, Jun 21 2009

Status

approved