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

1,2

Comments

See A357820 for more details.

Links

Table of n, a(n) for n=1..46.

Formula

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A001615, A173290, A357820 (numerators).

Similar sequence: A211178.

Sequence in context: A085296 A306364 A357819 * A367183 A214401 A009781

Adjacent sequences: A357818 A357819 A357820 * A357822 A357823 A357824

Keyword

nonn,frac

Author

Amiram Eldar, Oct 14 2022

Status

approved