A216152 A205957(n) where n is a nonprime number.

1, 2, 12, 48, 144, 1440, 34560, 483840, 7257600, 58060800, 3135283200, 125411328000, 2633637888000, 57940033536000, 5562243219456000, 27811216097280000, 723091618529280000, 6507824566763520000, 364438175738757120000, 327994358164881408000000

Offset: 1

Author

Peter Luschny, Sep 02 2012

Keywords

• nonn

Comments

The distinct values of A205957. Partial products of A216153.

a(1),...,a(10) are highly totient numbers (A097942) and products of distinct factorials (A058295). The author conjectures that this is true in general.

Links

• Peter Luschny, The von Mangoldt Transformation.

Crossrefs

Cf. A051451.

Programs

Mathematica

A205957[n_] := Exp[-Sum[MoebiusMu[p] Log[k/p], {k, 1, n}, {p, FactorInteger[k][[All, 1]]}]];
Table[A205957[n], {n, 0, 30}] // DeleteDuplicates (* Jean-François Alcover, Jul 08 2019 *)

Sage

# sorted(list(set([A205957(n) for n in (0..31)])))
def A216152_list(n) :
    C = filter(lambda k: not is_prime(k), (1..n))
    return [A205957(c) for c in C]
A216152_list(31)

Formula

a(n) = A205957(A018252(n)).