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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 29 00:02 EST 2023. Contains 359905 sequences. (Running on oeis4.)