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

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

(PARI) for(n=1, 150, print1(length(contfrac(sumdiv(n, d, 1/d))), ", "))

Crossrefs

Cf. A017665, A017666, A071864.

Sequence in context: A262815 A076494 A217721 * A030362 A007906 A044050

Adjacent sequences: A071859 A071860 A071861 * A071863 A071864 A071865

Keyword

nonn

Author

Benoit Cloitre, Jun 09 2002

Status

approved