A072457 Shadow transform of tetrahedral numbers A000292.

0, 1, 1, 1, 2, 3, 1, 3, 2, 1, 4, 3, 3, 3, 4, 3, 2, 3, 1, 3, 7, 2, 4, 3, 3, 3, 4, 1, 7, 3, 3, 3, 2, 2, 4, 9, 2, 3, 4, 3, 7, 3, 6, 3, 7, 2, 4, 3, 2, 3, 4, 4, 7, 3, 1, 9, 7, 4, 4, 3, 6, 3, 4, 4, 2, 9, 4, 3, 7, 3, 13, 3, 2, 3, 4, 2, 7, 9, 4, 3, 7, 1, 4, 3, 8, 9, 4, 2, 7, 3, 4, 9, 7, 3, 4, 9, 3, 3, 4, 3, 7, 3, 3, 3, 7

Offset: 0

Author

N. J. A. Sloane, Aug 02 2002

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..10000
• Lorenz Halbeisen and Norbert Hungerbuehler, Number theoretic aspects of a combinatorial function, Notes on Number Theory and Discrete Mathematics 5(4) (1999), 138-150. (ps, pdf); see Definition 7 for the shadow transform.
• OEIS Wiki, Shadow transform.
• N. J. A. Sloane, Transforms.

Crossrefs

Cf. A000292.

Programs

Maple

a:= n-> add(`if`(modp(j*(j+1)*(j+2)/6, n)=0, 1, 0), j=0..n-1):
seq(a(n), n=0..120);  # Alois P. Heinz, Sep 16 2019

Mathematica

a[n_] := Sum[If[Mod[j*(j+1)*(j+2)/6, n] == 0, 1, 0], {j, 0, n-1}];
Table[a[n], {n, 0, 120}] (* Jean-François Alcover, Jan 07 2025, after Alois P. Heinz *)