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A359030
Positive numbers that are the sum of cubes of three distinct integers in arithmetic progression.
2
9, 27, 36, 57, 72, 99, 132, 153, 216, 219, 243, 288, 297, 324, 369, 387, 405, 408, 456, 489, 495, 531, 576, 603, 612, 645, 684, 729, 792, 855, 867, 963, 972, 996, 1017, 1056, 1071, 1125, 1179, 1197, 1224, 1233, 1353, 1368, 1407, 1455, 1476, 1539, 1548, 1584, 1701, 1728, 1737, 1752, 1845, 1881
OFFSET
1,1
COMMENTS
Numbers that can be represented in at least one way as 3*a*(a^2 + 2*b^2) for positive integers a and b.
In contrast to A306213, the arithmetic progression need not consist only of positive numbers.
LINKS
EXAMPLE
a(4) = 57 is a term because 57 = (-2)^3 + 1^3 + 4^3 where (-2, 1, 3) are in arithmetic progression.
MAPLE
N:= 2000: # for terms <= N
L:= NULL:
for a from 1 while 3*a^3 <= N do
for b from 1 do
x:= 3*a*(a^2 + 2*b^2);
if x > N then break fi;
L:= L, x
od od:
sort(convert({L}, list));
CROSSREFS
Sequence in context: A340237 A216168 A036303 * A325299 A353238 A116455
KEYWORD
nonn
AUTHOR
Robert Israel, Dec 15 2022
STATUS
approved