A071862 - OEIS

A071862

Number of elements in the continued fraction for Sum_{d|n} 1/d.

1, 2, 2, 3, 2, 1, 2, 3, 3, 3, 2, 2, 2, 4, 4, 3, 2, 2, 2, 2, 4, 5, 2, 2, 3, 6, 3, 1, 2, 3, 2, 3, 3, 5, 5, 5, 2, 6, 5, 2, 2, 3, 2, 3, 5, 5, 2, 5, 3, 4, 4, 5, 2, 3, 4, 2, 4, 5, 2, 3, 2, 6, 6, 3, 6, 3, 2, 5, 5, 3, 2, 5, 2, 6, 7, 4, 3, 3, 2, 3, 3, 5, 2, 3, 6, 6, 6, 2, 2, 4, 3, 5, 6, 5, 4, 5, 2, 6, 6, 5, 2, 3, 2, 2, 5

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OFFSET

1,2

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..65537

FORMULA

It seems that Sum_{k=1..n} a(k) ~ C*n*log(n) with C = 0.6....

EXAMPLE

Sum_{d|48} 1/d = 31/12, whose continued fraction is [2, 1, 1, 2, 2] with 5 elements, hence a(48)=5.

MATHEMATICA

a[n_] := Length@ContinuedFraction[DivisorSigma[1, n]/n]; Array[a, 100] (* Amiram Eldar, Aug 30 2019 *)

PROG