A349497 a(n) is the smallest element in the continued fraction of the harmonic mean of the divisors of n.

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

Author

Amiram Eldar, Nov 20 2021

Keywords

• nonn

Examples

			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.
		

Links

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

Crossrefs

Cf. A001248, A001599, A001600, A099377, A099378, A129521, A349473.

Programs

Mathematica

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

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).