A343704 - OEIS

%I #24 Jul 29 2023 13:55:12

%S 766,810,827,829,865,883,981,1018,1025,1044,1070,1105,1108,1142,1145,

%T 1161,1168,1226,1233,1252,1259,1289,1350,1368,1376,1424,1431,1439,

%U 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

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

%C 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.

%H David Consiglio, Jr., <a href="/A343704/b343704.txt">Table of n, a(n) for n = 1..10000</a>

%e 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.

%t Select[Range@2000,Length@Select[PowersRepresentations[#,5,3],FreeQ[#,0]&]>2&] (* _Giorgos Kalogeropoulos_, Apr 26 2021 *)

%o (Python)

%o from itertools import combinations_with_replacement as cwr

%o from collections import defaultdict

%o keep = defaultdict(lambda: 0)

%o power_terms = [x**3 for x in range(1,50)]#n

%o for pos in cwr(power_terms,5):#m

%o     tot = sum(pos)

%o     keep[tot] += 1

%o rets = sorted([k for k,v in keep.items() if v >= 3])#s

%o for x in range(len(rets)):

%o     print(rets[x])

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

%K nonn,easy

%O 1,1

%A _David Consiglio, Jr._, Apr 26 2021