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A158978
a(n) = product of numbers k <= n such that not all proper divisors of k are divisors of n.
1
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).
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
KEYWORD
nonn
AUTHOR
Jaroslav Krizek, Apr 01 2009
EXTENSIONS
Edited and extended by Klaus Brockhaus, Apr 07 2009
STATUS
approved