

A274016


Choose the lexically first tuple of six nonincreasing positive integers (a, b, c, d, e, f) such that a*b*c + d*e*f = n. Then a(n) = a*b*c.


3



1, 2, 3, 4, 5, 6, 7, 8, 8, 10, 8, 12, 12, 14, 8, 16, 16, 18, 12, 20, 18, 22, 16, 24, 18, 26, 27, 27, 27, 27, 24, 27, 32, 27, 27, 36, 36, 27, 36, 40, 36, 42, 36, 27, 45, 45, 36, 48, 48, 48, 48, 45, 27, 54, 48, 48, 50, 58, 48, 60, 60, 36, 60, 64, 48, 64, 64, 60, 64, 63, 64
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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



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

(Python)
limit = 10000
res = [0 for i in range(limit1)]
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(limit1):
..print(i+2, res[i])


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS

New title, corrected a(32) and more terms added by Charlie Neder, Aug 13 2018


STATUS

approved



