A345088 - OEIS

%I #7 Jul 31 2021 23:41:41

%S 2562624,5618250,6525000,6755328,7374375,12742920,13581352,14027112,

%T 14288373,18443160,20500992,22783032,23113728,25305048,26936064,

%U 27131840,29515968,30205440,32835375,38269440,39317832,39339000,40189248,42144192,42183504,43077952

%N Numbers that are the sum of three third powers in exactly eight ways.

%C Differs from A345087 at term 10 because 14926248 = 2^3 + 33^3 + 245^3  = 11^3 + 185^3 + 203^3  = 14^3 + 32^3 + 245^3  = 50^3 + 113^3 + 236^3  = 71^3 + 89^3 + 239^3  = 74^3 + 189^3 + 196^3  = 89^3 + 185^3 + 197^3  = 98^3 + 148^3 + 219^3  = 105^3 + 149^3 + 217^3.

%H David Consiglio, Jr., <a href="/A345088/b345088.txt">Table of n, a(n) for n = 1..100</a>

%e 2562624 is a term because 2562624 = 7^3 + 35^3 + 135^3  = 7^3 + 63^3 + 131^3  = 11^3 + 99^3 + 115^3  = 16^3 + 45^3 + 134^3  = 29^3 + 102^3 + 112^3  = 35^3 + 59^3 + 131^3  = 50^3 + 84^3 + 121^3  = 68^3 + 71^3 + 122^3.

%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, 1000)]

%o for pos in cwr(power_terms, 3):

%o     tot = sum(pos)

%o     keep[tot] += 1

%o rets = sorted([k for k, v in keep.items() if v == 8])

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

%o     print(rets[x])

%Y Cf. A025328, A344738, A345085, A345087, A345120, A345153.

%K nonn

%O 1,1

%A _David Consiglio, Jr._, Jun 07 2021