A129353 A051731 * A115361.

1, 2, 1, 1, 0, 1, 3, 2, 0, 1, 1, 0, 0, 0, 1, 2, 1, 2, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 4, 3, 0, 2, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 2, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 3, 2, 3, 1, 0, 2, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1

Offset: 1

Author

Gary W. Adamson, Apr 10 2007

Keywords

• nonn
• tabl

Comments

The inverse Moebius transform of the first column of A115361 which is A209229 gives the first column of this sequence.

Examples

			First few rows of the triangle are:
  1;
  2, 1;
  1, 0, 1;
  3, 2, 0, 1;
  1, 0, 0, 0, 1;
  2, 1, 2, 0, 0, 1;
  1, 0, 0, 0, 0, 0, 1;
  4, 3, 0, 2, 0, 0, 0, 1;
  ...
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..1275

Crossrefs

Column 1 is A001511.

Row sums are A129628 (inverse Moebius transform of A001511).

Cf. A051731, A115361.

Programs

Maple

A129353 := proc(n,k)
        add( A051731(n,j)*A115361(j-1,k-1),j=k..n) ;
end proc: # R. J. Mathar, Jul 14 2012

Mathematica

T[n_, k_] := If[Mod[n, k] != 0, 0, 1 + IntegerExponent[n/k, 2]];
Table[T[n, k], {n, 1, 15}, {k, 1, n}] // Flatten (* Jean-François Alcover, Apr 08 2020, from PARI *)

PARI

T(n, k)={if(n%k, 0, 1 + valuation(n/k,2))} \\ Andrew Howroyd, Aug 04 2018

Formula

T(n,k) = A001511(n/k) for k | n, T(n,k) = 0 otherwise. - Andrew Howroyd, Aug 04 2018