A332207 a(n) is the number of 3-factorizations of n.

1, 1, 1, 2, 1, 2, 2, 2, 2, 3, 1, 3, 2, 3, 2, 4, 1, 4, 3, 3, 2, 4, 2, 5, 3, 3, 2, 5, 2, 6, 2, 3, 3, 6, 2, 6, 3, 4, 3, 6, 1, 6, 4, 5, 3, 5, 2, 7, 4, 5, 3, 6, 2, 8, 3, 4, 3, 8, 2, 8, 4, 4, 4, 8, 3, 7, 2, 6, 4, 9, 2, 8, 3, 5, 5, 6, 2, 10, 6, 6, 3, 7, 2, 10, 4, 5, 3, 10

Offset: 1

Author

Michel Marcus, Feb 07 2020

Keywords

• nonn

Comments

See Bingham link for definitions.

Links

• Giovanni Resta, Table of n, a(n) for n = 1..10000
• Aram Bingham, Ternary arithmetic, factorization, and the class number one problem, arXiv:2002.02059 [math.NT], 2020. See Table 1 p. 14.

Crossrefs

Cf. A014556.

Programs

Mathematica

a[n_] := Block[{c=0, z=1}, While[3 z^2 - 3 z + 1 <= n, c += Length@ Solve[ x y z - (x-1) (y-1) (z-1) == n && x >= y >= z, {x, y}, Integers]; z++]; c]; Array[a, 88] (* Giovanni Resta, Feb 07 2020 *)

Extensions

More terms from Giovanni Resta, Feb 07 2020