A349473 Irregular triangle read by rows: the n-th row contains the elements in the continued fraction of the harmonic mean of the divisors of n.

1, 1, 3, 1, 2, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 3, 2, 7, 2, 2, 13, 2, 4, 2, 1, 1, 5, 2, 1, 1, 3, 1, 1, 6, 2, 3, 2, 2, 2, 1, 1, 2, 1, 1, 2, 1, 1, 8, 2, 1, 3, 3, 1, 1, 9, 2, 1, 6, 2, 1, 1, 1, 2, 2, 2, 4, 1, 1, 11, 3, 5, 2, 2, 2, 1, 1, 2, 2, 2, 10, 2, 1, 2, 3, 3, 1, 1, 14

Offset

1,3

Comments

For an odd prime p > 3, the p-th row has a length 3 with a(p, 1) = a(p, 2) = 1 and a(p, 3) = (p-1)/2.

For a harmonic number m = A001599(k), the m-th row has a length 1 with a(k, 1) = A099377(m) = A001600(k).

Links

Table of n, a(n) for n=1..88.

Example

The first ten rows of the triangle are:
  1,
  1, 3,
  1, 2,
  1, 1, 2, 2,
  1, 1, 2,
  2,
  1, 1, 3,
  2, 7, 2,
  2, 13,
  2, 4, 2
  ...

Mathematica

row[n_] := ContinuedFraction[DivisorSigma[0, n] / DivisorSigma[-1, n]]; Table[row[k], {k, 1, 29}] // Flatten

Crossrefs

Cf. A001599, A001600, A099377, A099378.

Cf. A349474 (row lengths).

Sequence in context: A016569 A072801 A098872 * A167366 A139436 A212305

Adjacent sequences: A349470 A349471 A349472 * A349474 A349475 A349476

Keyword

nonn,tabf

Author

Amiram Eldar, Nov 19 2021

Status

approved