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

Author

Jaroslav Krizek, Apr 01 2009

Keywords

• nonn

Comments

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

Examples

			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.
		

Crossrefs

Cf. A159073, A034386.

Programs

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

Formula

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

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

Extensions

Edited by R. J. Mathar, Apr 06 2009

More terms from Klaus Brockhaus, Apr 07 2009