A133698 Triangle, diagonal = A001227 with the rest zeros.

1, 0, 1, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2

Offset: 1

Author

Gary W. Adamson, Sep 21 2007

Keywords

• nonn
• tabl

Comments

Lower triangular part of an infinite matrix with A001227 (number of odd divisors of n) as the main diagonal, and the rest filled with zeros. - Redacted from the original formula given by the author. - Antti Karttunen, Jan 18 2025

Examples

			First few rows of the triangle are:
  1;
  0, 1;
  0, 0, 2
  0, 0, 0, 1;
  0, 0, 0, 0, 2;
  0, 0, 0, 0, 0, 2;
  0, 0, 0, 0, 0, 0, 2;
  0, 0, 0, 0, 0, 0, 0, 1;
  0, 0, 0, 0, 0, 0, 0, 0, 3;
  0, 0, 0, 0, 0, 0, 0, 0, 0, 2;
  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2;
  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2;
  ...
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..22155; the first 210 rows of the triangle

Crossrefs

Cf. A001227, A130209, A133699.

Programs

PARI

A000265(n) = (n>>valuation(n,2));
A133698(n) = if(ispolygonal(n,3), numdiv(A000265((sqrtint(1+(n*8))-1)/2)), 0); \\ Antti Karttunen, Jan 18 2025

Extensions

Offset corrected from 0 to 1 and data section extended to a(105) by Antti Karttunen, Jan 18 2025