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

1,2

Links

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

Formula

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

Example

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

Mathematica

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

Prog

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

Crossrefs

Row sums of A129573.

Cf. A001227.

Sequence in context: A326201 A342625 A295569 * A323466 A130193 A084516

Adjacent sequences: A129571 A129572 A129573 * A129575 A129576 A129577

Keyword

nonn

Author

Gary W. Adamson, Apr 22 2007

Extensions

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

Status

approved