A158978 a(n) = product of numbers k <= n such that not all proper divisors of k are divisors of n.

1, 1, 1, 1, 4, 1, 24, 6, 192, 432, 17280, 10, 207360, 51840, 322560, 1360800, 696729600, 3225600, 12541132800, 39191040, 27869184000, 1316818944000, 115880067072000, 349272000, 2781121609728000, 17382010060800000

Offset: 1

Author

Jaroslav Krizek, Apr 01 2009

Keywords

• nonn

Comments

The empty product is 1.

For primes p, a(p) = A000142(p) / A034386(p).

Examples

			For n = 7 we have the following proper divisors of k <= n: {1}, {1}, {1}, {1, 2}, {1}, {1, 2, 3}, {1}. Only 4 and 6 have proper divisors that are not divisors of 7, viz. 2 and 2, 3. Hence a(7) = 4 * 6 = 24.
		

Crossrefs

Cf. A000040, A000142, A034386, A158976.

Programs

Magma

[ IsEmpty(S) select 1 else &*S where S is [ k: k in [1..n] | exists(t){ d: d in Divisors(k) | d ne k and d notin Divisors(n) } ]: n in [1..26] ];

Extensions

Edited and extended by Klaus Brockhaus, Apr 07 2009