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

Author

Amiram Eldar, Nov 19 2021

Keywords

• nonn
• tabf

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).

Examples

			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
  ...
		

Crossrefs

Cf. A001599, A001600, A099377, A099378.

Cf. A349474 (row lengths).

Programs

Mathematica

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