A357819 Denominators of the partial sums of the reciprocals of the Dedekind psi function (A001615).

1, 3, 12, 4, 12, 1, 8, 24, 24, 72, 72, 36, 252, 504, 126, 504, 504, 504, 2520, 840, 3360, 10080, 10080, 10080, 2016, 2016, 2016, 2016, 10080, 10080, 5040, 1260, 5040, 15120, 7560, 3780, 71820, 17955, 143640, 17955, 35910, 574560, 6320160, 6320160, 6320160, 6320160

Offset

1,2

Comments

See A357818 for more details.

Links

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

Formula

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

Mathematica

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

Prog

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

Crossrefs

Cf. A001615, A173290, A357818 (numerators).

Similar sequences: A048049, A104529, A212718.

Sequence in context: A227106 A085296 A306364 * A357821 A367183 A214401

Adjacent sequences: A357816 A357817 A357818 * A357820 A357821 A357822

Keyword

nonn,frac

Author

Amiram Eldar, Oct 14 2022

Status

approved