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A344196 Numbers that are the sum of six fifth powers in ten or more ways.

%I A344196 #37 May 10 2024 02:20:37
%S A344196 55302546200,89999127392,96110537743,104484239200,120492759200,
%T A344196 121258798144,127794946400,133364991375,135030535200,136156575744,
%U A344196 151305014432,155434423925,174388570400,177099008000,179272687000,180336745600,182844944832,184948721056,187873845500
%N A344196 Numbers that are the sum of six fifth powers in ten or more ways.
%H A344196 Sean A. Irvine, <a href="/A344196/b344196.txt">Table of n, a(n) for n = 1..61</a>
%e A344196 89999127392 =  4^5 + 36^5 + 39^5 +  40^5 +  90^5 + 153^5
%e A344196             =  8^5 + 21^5 + 90^5 + 109^5 + 119^5 + 135^5
%e A344196             =  8^5 + 28^5 + 98^5 + 102^5 + 104^5 + 142^5
%e A344196             = 10^5 + 38^5 + 74^5 + 102^5 + 118^5 + 140^5
%e A344196             = 13^5 + 51^5 + 64^5 +  98^5 + 112^5 + 144^5
%e A344196             = 18^5 + 44^5 + 66^5 +  98^5 + 112^5 + 144^5
%e A344196             = 18^5 + 52^5 + 72^5 +  78^5 + 118^5 + 144^5
%e A344196             = 28^5 + 60^5 + 63^5 +  65^5 + 124^5 + 142^5
%e A344196             = 36^5 + 53^5 + 62^5 +  63^5 + 129^5 + 139^5
%e A344196             = 39^5 + 41^5 + 64^5 +  91^5 +  98^5 + 149^5
%e A344196 so 89999127392 is a term.
%o A344196 (Python)
%o A344196 from itertools import combinations_with_replacement as cwr
%o A344196 from collections import defaultdict
%o A344196 keep = defaultdict(lambda: 0)
%o A344196 power_terms = [x**5 for x in range(1, 1000)]
%o A344196 for pos in cwr(power_terms, 6):
%o A344196     tot = sum(pos)
%o A344196     keep[tot] += 1
%o A344196     rets = sorted([k for k, v in keep.items() if v >= 10])
%o A344196     for x in range(len(rets)):
%o A344196         print(rets[x])
%Y A344196 Cf. A345567, A345643, A345723, A346365.
%K A344196 nonn
%O A344196 1,1
%A A344196 _David Consiglio, Jr._, Jun 25 2021