A332207 - OEIS

%I #9 Feb 07 2020 11:43:11

%S 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,

%T 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,

%U 4,9,2,8,3,5,5,6,2,10,6,6,3,7,2,10,4,5,3,10

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

%C See Bingham link for definitions.

%H Giovanni Resta, <a href="/A332207/b332207.txt">Table of n, a(n) for n = 1..10000</a>

%H Aram Bingham, <a href="https://arxiv.org/abs/2002.02059">Ternary arithmetic, factorization, and the class number one problem</a>, arXiv:2002.02059 [math.NT], 2020. See Table 1 p. 14.

%t 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 *)

%Y Cf. A014556.

%K nonn

%O 1,4

%A _Michel Marcus_, Feb 07 2020

%E More terms from _Giovanni Resta_, Feb 07 2020