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%I #11 Jul 08 2019 06:55:05
%S 1,2,12,48,144,1440,34560,483840,7257600,58060800,3135283200,
%T 125411328000,2633637888000,57940033536000,5562243219456000,
%U 27811216097280000,723091618529280000,6507824566763520000,364438175738757120000,327994358164881408000000
%N A205957(n) where n is a nonprime number.
%C The distinct values of A205957. Partial products of A216153.
%C a(1),...,a(10) are highly totient numbers (A097942) and products of distinct factorials (A058295). The author conjectures that this is true in general.
%H Peter Luschny, <a href="http://oeis.org/wiki/User:Peter_Luschny/VonMangoldtTransformation">The von Mangoldt Transformation.</a>
%F a(n) = A205957(A018252(n)).
%t A205957[n_] := Exp[-Sum[MoebiusMu[p] Log[k/p], {k, 1, n}, {p, FactorInteger[k][[All, 1]]}]];
%t Table[A205957[n], {n, 0, 30}] // DeleteDuplicates (* _Jean-François Alcover_, Jul 08 2019 *)
%o (Sage)
%o # sorted(list(set([A205957(n) for n in (0..31)])))
%o def A216152_list(n) :
%o C = filter(lambda k: not is_prime(k), (1..n))
%o return [A205957(c) for c in C]
%o A216152_list(31)
%Y Cf. A051451.
%K nonn
%O 1,2
%A _Peter Luschny_, Sep 02 2012
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