cp's OEIS Frontend

A346365 Numbers that are the sum of six fifth powers in exactly ten ways.

%I A346365 #14 May 11 2024 20:43:41
%S A346365 55302546200,89999127392,96110537743,104484239200,120492759200,
%T A346365 121258798144,127794946400,133364991375,135030535200,136156575744,
%U A346365 151305014432,155434423925,174388570400,177099008000,179272687000,182844944832,184948721056,187873845500
%N A346365 Numbers that are the sum of six fifth powers in exactly ten ways.
%C A346365 This sequence differs from A344196:
%C A346365 180336745600 = 48^5 + 54^5 +  66^5 +  66^5 + 112^5 + 174^5
%C A346365              =  9^5 + 21^5 +  93^5 + 112^5 + 117^5 + 168^5
%C A346365              = 11^5 + 44^5 +  73^5 +  92^5 + 133^5 + 167^5
%C A346365              = 15^5 + 81^5 +  94^5 +  95^5 + 129^5 + 166^5
%C A346365              =  1^5 + 49^5 +  62^5 + 107^5 + 138^5 + 163^5
%C A346365              = 35^5 + 69^5 +  75^5 +  98^5 + 141^5 + 162^5
%C A346365              = 18^5 + 81^5 + 105^5 + 112^5 + 135^5 + 159^5
%C A346365              = 14^5 + 50^5 +  62^5 +  86^5 + 150^5 + 158^5
%C A346365              =  2^5 + 52^5 +  54^5 + 108^5 + 146^5 + 158^5
%C A346365              = 14^5 + 22^5 +  66^5 + 118^5 + 142^5 + 158^5
%C A346365              =  4^5 + 50^5 +  58^5 + 102^5 + 150^5 + 156^5,
%C A346365 so 180336745600 is in A344196, but is not in this sequence.
%H A346365 Sean A. Irvine, <a href="/A346365/b346365.txt">Table of n, a(n) for n = 1..57</a>
%e A346365 55302546200 = 34^5 + 38^5 + 50^5 + 57^5 + 95^5 + 136^5
%e A346365             = 23^5 + 49^5 + 61^5 + 69^5 + 107^5 + 131^5
%e A346365             = 24^5 + 37^5 + 63^5 + 81^5 + 104^5 + 131^5
%e A346365             = 21^5 + 35^5 + 60^5 + 94^5 + 100^5 + 130^5
%e A346365             = 57^5 + 60^5 + 71^5 + 75^5 + 109^5 + 128^5
%e A346365             = 19^5 + 37^5 + 56^5 + 96^5 + 104^5 + 128^5
%e A346365             = 35^5 + 41^5 + 53^5 + 69^5 + 115^5 + 127^5
%e A346365             = 16^5 + 49^5 + 53^5 + 83^5 + 112^5 + 127^5
%e A346365             = 35^5 + 37^5 + 40^5 + 88^5 + 119^5 + 121^5
%e A346365             = 11^5 + 24^5 + 71^5 + 104^5 + 109^5 + 121^5
%e A346365 so 55302546200 is a term.
%o A346365 (Python)
%o A346365 from itertools import combinations_with_replacement as cwr
%o A346365 from collections import defaultdict
%o A346365 keep = defaultdict(lambda: 0)
%o A346365 power_terms = [x**5 for x in range(1, 1000)]
%o A346365 for pos in cwr(power_terms, 6):
%o A346365     tot = sum(pos)
%o A346365     keep[tot] += 1
%o A346365     rets = sorted([k for k, v in keep.items() if v == 10])
%o A346365     for x in range(len(rets)):
%o A346365         print(rets[x])
%Y A346365 Cf. A344196, A345822, A346259, A346364.
%K A346365 nonn
%O A346365 1,1
%A A346365 _David Consiglio, Jr._, Jul 18 2021