A359030 Positive numbers that are the sum of cubes of three distinct integers in arithmetic progression.

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

Author

Robert Israel, Dec 15 2022

Keywords

• nonn

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.

Examples

			a(4) = 57 is a term because 57 = (-2)^3 + 1^3 + 4^3 where (-2, 1, 3) are in arithmetic progression.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A306213, A359078.

Programs

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));