A158977 Product of the numbers k in the range 1 <= k <= n such that the proper divisors of k are a subset of the proper divisors of n.

1, 2, 6, 24, 30, 720, 210, 6720, 1890, 8400, 2310, 47900160, 30030, 1681680, 4054050, 15375360, 510510, 1984862880, 9699690, 62078016000, 1833241410, 853572720, 223092870, 1776404640890880, 5577321750, 23201658480, 54211567410

Offset

1,2

Comments

Here, proper divisors include 1 but not the argument (k or n, respectively) in the divisor set, as counted in A032741.

Links

Table of n, a(n) for n=1..27.

Formula

If p is prime, a(p) = A034386(p).

a(n)*A158978(n) = A000142(n). - R. J. Mathar, Apr 06 2009

Example

a(8) = 6720 is the product of the 7 numbers k: 1 {1}, 2 {1}, 3 {1}, 4 {1, 2}, 5 {1}, 7 {1}, 8 {1, 2, 4} with divisor set that are subsets of {1, 2, 4} for n = 8. 1 * 2 * 3 * 4 * 5 * 7 * 8 = 6720.

Prog

(Magma) [ &*[ k: k in [1..n] | forall(t){ d: d in Divisors(k) | d eq k or d in Divisors(n) } ]: n in [1..27] ]; // Klaus Brockhaus, Apr 07 2009

Crossrefs

Cf. A159073, A034386.

Sequence in context: A377710 A066332 A069141 * A165823 A263690 A137326

Adjacent sequences: A158974 A158975 A158976 * A158978 A158979 A158980

Keyword

nonn

Author

Jaroslav Krizek, Apr 01 2009

Extensions

Edited by R. J. Mathar, Apr 06 2009

More terms from Klaus Brockhaus, Apr 07 2009

Status

approved