A332770 - OEIS

%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