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

1,6

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

Links

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

Example

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;
  ...

Prog

(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

Crossrefs

Cf. A001227, A130209, A133699.

Sequence in context: A037881 A024326 A287619 * A219488 A370813 A129251

Adjacent sequences: A133695 A133696 A133697 * A133699 A133700 A133701

Keyword

nonn,tabl

Author

Gary W. Adamson, Sep 21 2007

Extensions

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

Status

approved