A129573 -id:A129573 - cp's OEIS frontend

A129574 Number of odd divisors of n plus the number of odd divisors of n - 1.

1, 2, 3, 3, 3, 4, 4, 3, 4, 5, 4, 4, 4, 4, 6, 5, 3, 5, 5, 4, 6, 6, 4, 4, 5, 5, 6, 6, 4, 6, 6, 3, 5, 6, 6, 7, 5, 4, 6, 6, 4, 6, 6, 4, 8, 8, 4, 4, 5, 6, 7, 6, 4, 6, 8, 6, 6, 6, 4, 6, 6, 4, 8, 7, 5, 8, 6, 4, 6, 8, 6, 5, 5, 4, 8, 8, 6, 8, 6, 4, 7, 7, 4, 6, 8, 6, 6, 6, 4, 8

Offset: 1

Gary W. Adamson, Apr 22 2007

nonn

			a(4) = 3 = sum of row 4 of triangle A129573: (1 + 0 + 1 + 1).

Andrew Howroyd, Table of n, a(n) for n = 1..1000

Row sums of A129573.

Cf. A001227.

Join[{1},Table[Total[Mod[Divisors[n],2]]+Total[Mod[Divisors[n-1],2]],{n,2,90}]] (* James C. McMahon, Jan 31 2025 *)

a(n)=numdiv(n >> valuation(n,2)) + if(n > 1, numdiv((n-1) >> valuation(n-1,2))) \\ Andrew Howroyd, Aug 10 2018

a(n) = A001227(n) + A001227(n-1). - Andrew Howroyd, Aug 10 2018

Name changed and terms a(11) and beyond from Andrew Howroyd, Aug 10 2018

A129572 A129372 * A097806.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1

Offset: 1

Gary W. Adamson, Apr 22 2007

Row sums = A086374: (1, 2, 3, 2, 3, 4, 3, 2, 5, 4, ...). A129573 = A097806 * A129372.

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

Cf. A129372, A097806, A086374, A129573.

A129372 * A097806 as infinite lower triangular matrices.

cp's OEIS Frontend

A129574 Number of odd divisors of n plus the number of odd divisors of n - 1.

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