Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%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