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 A071862 Number of elements in the continued fraction for Sum_{d|n} 1/d. 5
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified May 12 10:54 EDT 2021. Contains 343821 sequences. (Running on oeis4.)