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A344364 Numbers that are the sum of three fourth powers in five or more ways. 6

%I

%S 292965218,779888018,1010431058,1110995522,1234349298,1289202642,

%T 1500533762,1665914642,1948502738,2158376402,2373191618,2636686962,

%U 2689817858,2935465442,3019732898,3205282178,3642994082,3831800882,4162186322,4324686002,4687443488,5064808658

%N Numbers that are the sum of three fourth powers in five or more ways.

%H Sean A. Irvine, <a href="/A344364/b344364.txt">Table of n, a(n) for n = 1..10000</a>

%e 292965218 is a member of this sequence because 292965218 = 2^4 + 109^4 + 111^4 = 21^4 + 98^4 + 119^4 = 27^4 + 94^4 + 121^4 = 34^4 + 89^4 + 123^4 = 49^4 + 77^4 + 126^4 = 61^4 + 66^4 + 127^4 (actually has 6 representations, so is a member of this sequence but not of A344365).

%e 1234349298 is a member of this sequence because 1234349298 = 7^4 + 154^4 + 161^4 = 26^4 + 143^4 + 169^4 = 61^4 + 118^4 + 179^4 = 74^4 + 107^4 + 181^4 = 91^4 + 91^4 + 182^4.

%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**4 for x in range(1, 500)]

%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 >= 5])

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

%o print(rets[x])

%Y Cf. A343967, A344277, A344356, A344365, A344647.

%K nonn

%O 1,1

%A _Sean A. Irvine_, May 15 2021

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Last modified October 6 20:00 EDT 2022. Contains 357270 sequences. (Running on oeis4.)