

A349474


a(n) is the length of the continued fraction of the harmonic mean of the divisors of n.


6



1, 2, 2, 4, 3, 1, 3, 3, 2, 3, 3, 4, 3, 2, 2, 7, 3, 4, 3, 3, 5, 3, 3, 2, 6, 3, 4, 1, 3, 2, 3, 2, 3, 4, 3, 8, 3, 4, 5, 4, 3, 2, 3, 2, 3, 4, 3, 5, 6, 4, 3, 4, 3, 4, 2, 5, 5, 7, 3, 3, 3, 5, 7, 7, 3, 3, 3, 3, 3, 3, 3, 4, 3, 5, 7, 4, 4, 4, 3, 4, 6, 6, 3, 2, 4, 6, 3
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OFFSET

1,2


COMMENTS

a(n) = 1 if and only if n is a harmonic number (A001599).
a(n) <= 2 if and only if n is in A348865.


LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000


EXAMPLE

a(1) = 1 since the harmonic mean of the divisors of 1 is 1 and its continued fraction has 1 element, {1}.
a(2) = 2 since the harmonic mean of the divisors of 2 is 4/3 = 1 + 1/3 and its continued fraction has 2 elements, {1, 3}.
a(4) = 4 since the harmonic mean of the divisors of 4 is 12/7 = 1 + 1/(1 + 1/(2 + 1/2)) and its continued fraction has 4 elements, {1, 1, 2, 2}.


MATHEMATICA

a[n_] := Length @ ContinuedFraction[DivisorSigma[0, n] / DivisorSigma[1, n]]; Array[a, 100]


CROSSREFS

Row length of A349473.
Cf. A001599, A071862, A099377, A099378, A348865.
Sequence in context: A252040 A084896 A011388 * A105114 A166284 A098086
Adjacent sequences: A349471 A349472 A349473 * A349475 A349476 A349477


KEYWORD

nonn


AUTHOR

Amiram Eldar, Nov 19 2021


STATUS

approved



