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) = abc
<Calculations done by hand - can someone please confirm before posting>
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)
#by Charlie Neder, using an algorithm from David A. Corneth, Aug 14 2018
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])
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