A338667 Numbers that are the sum of two positive cubes in exactly one way.

2, 9, 16, 28, 35, 54, 65, 72, 91, 126, 128, 133, 152, 189, 217, 224, 243, 250, 280, 341, 344, 351, 370, 407, 432, 468, 513, 520, 539, 559, 576, 637, 686, 728, 730, 737, 756, 793, 854, 855, 945, 1001, 1008, 1024, 1027, 1064, 1072, 1125, 1216, 1241, 1332, 1339, 1343, 1358, 1395, 1456, 1458, 1512, 1547, 1674, 1736

Offset

1,1

Comments

This sequence differs from A003325 at term 61: A003325(61) = 1729 is the famous Ramanujan taxicab number and is excluded from this sequence because it is the sum of two cubes in two distinct ways.

Links

David Consiglio, Jr., Table of n, a(n) for n = 1..20000

Example

35 is a term of this sequence because 2^3 + 3^3 = 8 + 27 = 35 and this is the one and only way to express 35 as the sum of two cubes.

Mathematica

Select[Range@2000, Length[s=PowersRepresentations[#, 2, 3]]==1&&And@@(#>0&@@@s)&] (* Giorgos Kalogeropoulos, Apr 24 2021 *)

Prog

(Python)
from itertools import combinations_with_replacement as cwr
from collections import defaultdict
from bisect import bisect_left as bisect
keep = defaultdict(lambda: 0)
power_terms = [x**3 for x in range(1, 1000)]
for pos in cwr(power_terms, 2):
    tot = sum(pos)
    keep[tot] += 1
rets = sorted([k for k, v in keep.items() if v == 1])
for x in range(len(rets)):
    print(rets[x])

Crossrefs

Cf. A003325, A025284, A025395, A343708, A344187.

Sequence in context: A085960 A051386 A003325 * A101420 A275498 A248434

Adjacent sequences: A338664 A338665 A338666 * A338668 A338669 A338670

Keyword

nonn,easy

Author

David Consiglio, Jr., Apr 22 2021

Status

approved