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

Author

David Consiglio, Jr., Apr 26 2021

Keywords

• nonn
• easy

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.

Examples

			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.
		

Links

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

Crossrefs

Cf. A003328, A025406, A048927, A343704, A344238, A344795, A345511.

Programs

Mathematica

Select[Range@1000,Length@Select[PowersRepresentations[#,5,3],FreeQ[#,0]&]>1&] (* Giorgos Kalogeropoulos, Apr 26 2021 *)

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])