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

1,5

Comments

The empty product is 1.

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

Links

Table of n, a(n) for n=1..26.

Example

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.

Prog

(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] ];

Crossrefs

Cf. A000040, A000142, A034386, A158976.

Sequence in context: A057869 A337204 A166027 * A128417 A257532 A183875

Adjacent sequences: A158975 A158976 A158977 * A158979 A158980 A158981

Keyword

nonn

Author

Jaroslav Krizek, Apr 01 2009

Extensions

Edited and extended by Klaus Brockhaus, Apr 07 2009

Status

approved