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

Author

Benoit Cloitre, Jun 09 2002

Keywords

• nonn

Examples

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

Links

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

Crossrefs

Cf. A017665, A017666, A071864.

Programs

Mathematica

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

PARI

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

Formula

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