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%I #4 Sep 08 2022 08:45:43
%S 1,1,1,1,4,1,24,6,192,432,17280,10,207360,51840,322560,1360800,
%T 696729600,3225600,12541132800,39191040,27869184000,1316818944000,
%U 115880067072000,349272000,2781121609728000,17382010060800000
%N a(n) = product of numbers k <= n such that not all proper divisors of k are divisors of n.
%C The empty product is 1.
%C For primes p, a(p) = A000142(p) / A034386(p).
%e 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.
%o (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] ];
%Y Cf. A000040, A000142, A034386, A158976.
%K nonn
%O 1,5
%A _Jaroslav Krizek_, Apr 01 2009
%E Edited and extended by _Klaus Brockhaus_, Apr 07 2009
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