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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 (list; graph; refs; listen; history; text; internal format)
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
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
Sequence in context: A245338 A160755 A017873 * A291572 A265541 A128557
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

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Last modified July 18 01:34 EDT 2024. Contains 374377 sequences. (Running on oeis4.)