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A349497
a(n) is the smallest element in the continued fraction of the harmonic mean of the divisors of n.
2
1, 1, 1, 1, 1, 2, 1, 2, 2, 2, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 2, 1, 3, 1, 2, 1, 3, 1, 3, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 3, 2, 1, 1, 1, 1, 2, 1, 2, 1, 1, 3, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 3, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 2, 1, 1, 1
OFFSET
1,6
LINKS
FORMULA
a(p) = 1 for a prime p.
a(p^2) = 1 for a prime p != 3.
a(A129521(n)) = 1 for n > 3.
For a harmonic number m = A001599(k), a(m) = A099377(m) = A001600(k).
EXAMPLE
a(2) = 1 since the continued fraction of the harmonic mean of the divisors of 2, 4/3 = 1 + 1/3, has 2 elements, {1, 3}, and the smallest of them is 1.
MATHEMATICA
a[n_] := Min[ContinuedFraction[DivisorSigma[0, n] / DivisorSigma[-1, n]]]; Array[a, 100]
KEYWORD
nonn
AUTHOR
Amiram Eldar, Nov 20 2021
STATUS
approved