

A359055


Numbers that can be represented in more than one way as the sum of cubes of three distinct positive numbers in arithmetic progression.


1



5643, 12384, 31977, 45144, 99072, 123849, 152361, 153792, 255816, 259776, 269739, 274968, 334368, 361152, 477576, 500445, 705375, 792576, 863379, 912339, 928017, 950931, 990792, 1090584, 1218888, 1230336, 1548000, 1629144, 1700424, 1737252, 1799523, 1813512, 1935549, 1941192, 2046528, 2078208
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OFFSET

1,1


COMMENTS

Numbers k such that there are at least two pairs of positive numbers (a,d) such that k = a^3 + (a+d)^3 + (a+2d)^3.
The first term that has three such representations is 255816 = 8^3 + 34^3 + 60^3 = 18^3 + 38^3 + 58^3 = 43^3 + 44^3 + 45^3.
346380489216 has four such representations: 1188^3 + 3888^3 + 6588^3, 1728^3 + 4104^3 + 6480^3, 4248^3 + 4824^3 + 5400^3 and 4665^3 + 4864^3 + 5063^3. It might not be the first.


LINKS



EXAMPLE

a(1) = 5643 is a term because 5643 = 1^3 + (1+8)^3 + (1+2*8)^3 = 6^3 + (6+5)^3 + (6+2*5)^3.


MAPLE

N:= 10^7: # to get terms <= N
S:= {}: S2:= {}:
for a from 1 while a^3 + (a+1)^3 + (a+2)^3 <= N do
for d from 1 do
x:= a^3 + (a+d)^3 + (a+2*d)^3;
if x > N then break fi;
if member(x, S) then S2:= S2 union {x} fi;
S:= S union {x}
od od:
sort(convert(S, list));


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



