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

1,6

Links

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

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]

Crossrefs

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

Sequence in context: A138516 A180580 A026513 * A106028 A105307 A281012

Adjacent sequences: A349494 A349495 A349496 * A349498 A349499 A349500

Keyword

nonn

Author

Amiram Eldar, Nov 20 2021

Status

approved