A343702 Numbers that are the sum of five positive cubes in two or more ways.

157, 220, 227, 246, 253, 260, 267, 279, 283, 286, 305, 316, 323, 342, 344, 361, 368, 377, 379, 384, 403, 410, 435, 440, 442, 468, 475, 487, 494, 501, 523, 530, 531, 549, 562, 568, 586, 592, 594, 595, 599, 602, 621, 625, 640, 647, 657, 658, 683, 703, 710, 712, 719, 729, 731, 738, 745, 752, 759, 764, 766, 771, 773, 778, 785

Offset

1,1

Comments

This sequence differs from A048927:

766 = 1^3 + 1^3 + 2^3 + 3^3 + 9^3

= 1^3 + 4^3 + 4^3 + 5^3 + 8^3

= 2^3 + 2^3 + 4^3 + 7^3 + 7^3.

So 766 is a term, but not a term of A048927.

Links

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

Example

227 = 1^3 + 1^3 + 1^3 + 2^3 + 6^3
    = 2^3 + 3^3 + 4^3 + 4^3 + 4^3
so 227 is a term of this sequence.

Mathematica

Select[Range@1000, Length@Select[PowersRepresentations[#, 5, 3], FreeQ[#, 0]&]>1&] (* 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, 50)]#n
for pos in cwr(power_terms, 5):#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. A003328, A025406, A048927, A343704, A344238, A344795, A345511.

Sequence in context: A007356 A236537 A048927 * A163490 A142063 A151739

Adjacent sequences: A343699 A343700 A343701 * A343703 A343704 A343705

Keyword

nonn,easy

Author

David Consiglio, Jr., Apr 26 2021

Status

approved