A343708 Numbers that are the sum of two positive cubes in exactly two ways.

1729, 4104, 13832, 20683, 32832, 39312, 40033, 46683, 64232, 65728, 110656, 110808, 134379, 149389, 165464, 171288, 195841, 216027, 216125, 262656, 314496, 320264, 327763, 373464, 402597, 439101, 443889, 513000, 513856, 515375, 525824, 558441, 593047, 684019, 704977, 805688, 842751, 885248, 886464

Offset

1,1

Comments

This sequence differs from A001235 at term 455 because 87539319 = 167^3 + 436^3 = 228^3 + 423^3 = 255^3 + 414^3 = A011541(3). Thus, this term is not in this sequence but is in A001235.

Links

David Consiglio, Jr., Table of n, a(n) for n = 1..1000

Example

13832 is in this sequence because 13832 = 2^3 + 24^3 = 18^3 + 20^3.

Mathematica

Select[Range@70000, Length@Select[PowersRepresentations[#, 2, 3], FreeQ[#, 0]&]==2&] (* Giorgos Kalogeropoulos, Apr 26 2021 *)

Prog

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

Crossrefs

Cf. A001235, A025285, A025396, A338667, A344804.

Sequence in context: A138129 A242880 A001235 * A018850 A062924 A350270

Adjacent sequences: A343705 A343706 A343707 * A343709 A343710 A343711

Keyword

nonn,easy

Author

David Consiglio, Jr., Apr 26 2021

Status

approved