A071865 Smallest k such that the simple continued fraction for Sum(d|k, 1/d) contains exactly n elements.

1, 2, 4, 14, 22, 26, 75, 195, 330, 324, 935, 1598, 3422, 3663, 10191, 14066, 12099, 53661, 121555, 182169, 235509, 307615, 633945, 2097595, 2072198, 2643298, 6544282, 8675343, 13670722, 17573794, 85112326, 77295778, 235873898, 362150458, 544042486, 1457255474

Offset

1,2

Links

Table of n, a(n) for n=1..36.

Example

sum(d|195, 1/d) = 112/65 and 112/65 continued fraction is [1, 1, 2, 1, 1, 1, 1, 3] which contains 8 elements. There is no smaller number than 195 with this property hence a(8)=195.

Mathematica

a = Table[0, {50}]; Do[b = Length[ ContinuedFraction[ Apply[ Plus, 1/Divisors[n]]]]; If[ a[[b]] == 0, a[[b]] = n], {n, 1, 10^7}]

Prog

(PARI) for(n=1, 21, s=1; while(length(contfrac(sumdiv(s, d, 1/d)))<n, s++); print1(s, ", "))

Crossrefs

Cf. A071862.

Sequence in context: A032309 A008519 A243934 * A127596 A111871 A291079

Adjacent sequences: A071862 A071863 A071864 * A071866 A071867 A071868

Keyword

easy,nonn

Author

Benoit Cloitre, Jun 09 2002

Extensions

More terms from Robert G. Wilson v, Jun 11 2002

a(29)-a(36) from Michel Marcus, Sep 17 2012

Status

approved