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A343704 Numbers that are the sum of five positive cubes in three or more ways. 8
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 (list; graph; refs; listen; history; text; internal format)
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

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

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Last modified January 31 17:49 EST 2023. Contains 359980 sequences. (Running on oeis4.)