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%I #10 Jun 10 2021 21:03:29
%S 1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,2,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,
%T 2,1,1,1,1,1,1,1,1,2,1,1,3,1,1,1,1,1,2,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,
%U 1,2,1,2,1,1,1,1,2,2,1,1,1,1,1,2,1,1,2
%N a(n) is the number of ways to write A180045(n) as (x*y+1)*(x*z+1) with x > y > z > 1.
%H Robert Israel, <a href="/A332770/b332770.txt">Table of n, a(n) for n = 1..10000</a>
%H Rémy Sigrist, <a href="/A332770/a332770_2.txt">C program for A332770</a>
%e The first terms, alongside A180045(n), are:
%e n a(n) A180045(n)
%e -- ---- ---------------------------------------
%e 1 1 28 = (3*2+1)*(3*1+1)
%e 2 1 45 = (4*2+1)*(4*1+1)
%e 3 1 65 = (4*3+1)*(4*1+1)
%e 4 1 66 = (5*2+1)*(5*1+1)
%e 5 1 91 = (6*2+1)*(6*1+1)
%e 6 1 96 = (5*3+1)*(5*1+1)
%e 7 1 117 = (4*3+1)*(4*2+1)
%e 8 1 120 = (7*2+1)*(7*1+1)
%e 9 1 126 = (5*4+1)*(5*1+1)
%e 10 1 133 = (6*3+1)*(6*1+1)
%e 11 1 153 = (8*2+1)*(8*1+1)
%e 12 1 175 = (6*4+1)*(6*1+1)
%e 13 2 176 = (5*3+1)*(5*2+1) = (7*3+1)*(7*1+1)
%p N:= 20000: # for a(n) where A180045(n) <= N
%p V:= Vector(N):
%p for x from 3 while (2*x+1)*(x+1) <= N do
%p for y from 2 to x-1 while (x*y+1)*(x+1) <= N do
%p for z from 1 to y-1 do
%p v:= (x*y+1)*(x*z+1);
%p if v > N then break fi;
%p V[v]:= V[v]+1;
%p od od od:
%p subs(0=NULL,convert(V,list)); # _Robert Israel_, Jun 10 2021
%o (C) See Links section.
%Y Cf. A180045.
%K nonn
%O 1,13
%A _Rémy Sigrist_, Feb 23 2020
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