A343704 Numbers that are the sum of five positive cubes in three or more ways.

766, 810, 827, 829, 865, 883, 981, 1018, 1025, 1044, 1070, 1105, 1108, 1142, 1145, 1161, 1168, 1226, 1233, 1252, 1259, 1289, 1350, 1368, 1376, 1424, 1431, 1439, 1441, 1457, 1461, 1487, 1492, 1494, 1522, 1529, 1531, 1538, 1548, 1550, 1555, 1568, 1583, 1585, 1587, 1590, 1592, 1593, 1594, 1609, 1611, 1613, 1639

Offset

1,1

Comments

This sequence differs from A343705 at term 20 because 1252 = 1^3+1^3+5^3+5^3+10^3= 1^3+2^3+3^3+6^3+10^3 = 3^3+3^3+7^3+7^3+8^3 = 3^3+4^3+6^3+6^3+9^3. Thus this term is in this sequence but not A343705.

Links

David Consiglio, Jr., Table of n, a(n) for n = 1..10000

Example

827 is a member of this sequence because 827 = 1^3 + 4^3 + 5^3 + 5^3 + 8^3 = 2^3 + 2^3 + 5^3 + 7^3 + 7^3 = 2^3 + 3^3 + 4^3 + 6^3 + 8^3.

Mathematica

Select[Range@2000, Length@Select[PowersRepresentations[#, 5, 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, 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 >= 3])#s
for x in range(len(rets)):
    print(rets[x])

Crossrefs

Cf. A025407, A343702, A343705, A344034, A344243, A344796, A345512.

Sequence in context: A319741 A329757 A127206 * A343705 A247486 A125109

Adjacent sequences: A343701 A343702 A343703 * A343705 A343706 A343707

Keyword

nonn,easy

Author

David Consiglio, Jr., Apr 26 2021

Status

approved