OFFSET
2,2
COMMENTS
Previous name: Numbers n such that n is the sum of the volumes of two rectangular cuboids, abc + def where a >= b >= c >= d >= e >= f >= 1. a(n) = abc. (Additional constraints below)
In the case of multiple solutions:
a is made as small as possible - then
b is made as small as possible - then
c is made as small as possible - then
...
f is made as small as possible.
a(n) = a*b*c.
LINKS
Charlie Neder, Table of n, a(n) for n = 2..10000
David A. Corneth, PARI program
EXAMPLE
a(33) = 27 because 3*3*3 + 3*2*1 = 33.
a(33) != 32 because although 4*4*2 + 1*1*1 = 33 in the case of multiple solutions, you must choose a minimal value for a.
PROG
(PARI) \\ See Corneth link. David A. Corneth, Aug 14 2018
(Python)
limit = 10000
res = [0 for i in range(limit-1)]
a = 1
while not all(i > 0 for i in res):
for b in range(1, a+1):
for c in range(1, b+1):
for d in range(1, c+1):
for e in range(1, d+1):
for f in range(1, e+1):
if a*b*c + d*e*f in range(2, limit+1):
if not res[a*b*c + d*e*f - 2]:
res[a*b*c + d*e*f - 2] = a*b*c
a += 1
for i in range(limit-1):
print(i+2, res[i]) # Charlie Neder, using an algorithm from David A. Corneth, Aug 14 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Gordon Hamilton, Jun 06 2016
EXTENSIONS
New title, corrected a(32) and more terms added by Charlie Neder, Aug 13 2018
STATUS
approved