A357821 Denominators of the partial alternating sums of the reciprocals of the Dedekind psi function (A001615).

1, 3, 12, 4, 12, 6, 24, 8, 24, 72, 72, 18, 63, 504, 63, 504, 168, 504, 2520, 2520, 10080, 1120, 3360, 3360, 672, 224, 2016, 2016, 10080, 10080, 5040, 2520, 5040, 15120, 1890, 7560, 143640, 143640, 17955, 143640, 143640, 574560, 6320160, 6320160, 6320160, 6320160

Offset: 1

Author

Amiram Eldar, Oct 14 2022

Keywords

• nonn
• frac

Comments

See A357820 for more details.

Crossrefs

Cf. A001615, A173290, A357820 (numerators).

Similar sequence: A211178.

Programs

Mathematica

psi[n_] := n * Times @@ (1 + 1/Transpose[FactorInteger[n]][[1]]); psi[1] = 1; Denominator[Accumulate[1/Array[(-1)^(# + 1)*psi[#] &, 50]]]

PARI

f(n) = n * sumdivmult(n, d, issquarefree(d)/d); \\ A001615
a(n) = denominator(sum(k=1, n, (-1)^(k+1)/f(k))); \\ Michel Marcus, Oct 15 2022

Formula

a(n) = denominator(Sum_{k=1..n} (-1)^(k+1)/psi(k)).