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A332770
a(n) is the number of ways to write A180045(n) as (x*y+1)*(x*z+1) with x > y > z > 1.
2
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, 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, 1, 2, 1, 2, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 2, 1, 1, 2
OFFSET
1,13
LINKS
EXAMPLE
The first terms, alongside A180045(n), are:
n a(n) A180045(n)
-- ---- ---------------------------------------
1 1 28 = (3*2+1)*(3*1+1)
2 1 45 = (4*2+1)*(4*1+1)
3 1 65 = (4*3+1)*(4*1+1)
4 1 66 = (5*2+1)*(5*1+1)
5 1 91 = (6*2+1)*(6*1+1)
6 1 96 = (5*3+1)*(5*1+1)
7 1 117 = (4*3+1)*(4*2+1)
8 1 120 = (7*2+1)*(7*1+1)
9 1 126 = (5*4+1)*(5*1+1)
10 1 133 = (6*3+1)*(6*1+1)
11 1 153 = (8*2+1)*(8*1+1)
12 1 175 = (6*4+1)*(6*1+1)
13 2 176 = (5*3+1)*(5*2+1) = (7*3+1)*(7*1+1)
MAPLE
N:= 20000: # for a(n) where A180045(n) <= N
V:= Vector(N):
for x from 3 while (2*x+1)*(x+1) <= N do
for y from 2 to x-1 while (x*y+1)*(x+1) <= N do
for z from 1 to y-1 do
v:= (x*y+1)*(x*z+1);
if v > N then break fi;
V[v]:= V[v]+1;
od od od:
subs(0=NULL, convert(V, list)); # Robert Israel, Jun 10 2021
PROG
(C) See Links section.
CROSSREFS
Cf. A180045.
Sequence in context: A344590 A111616 A299152 * A113120 A154843 A062557
KEYWORD
nonn
AUTHOR
Rémy Sigrist, Feb 23 2020
STATUS
approved