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

1,4

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.

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 *)

Crossrefs

Cf. A014556.

Sequence in context: A215904 A083552 A326034 * A339929 A176835 A353865

Adjacent sequences: A332204 A332205 A332206 * A332208 A332209 A332210

Keyword

nonn

Author

Michel Marcus, Feb 07 2020

Extensions

More terms from Giovanni Resta, Feb 07 2020

Status

approved