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Numbers that are the sum of four fourth powers in six or more ways.
7

%I #15 Jul 31 2021 18:22:02

%S 3847554,5624739,6044418,6576339,6593538,6899603,9851058,10456338,

%T 11645394,12378018,13155858,13638738,16020018,16408434,16990803,

%U 19081089,20622338,20649603,20755218,20795763,22673634,23056803,24174003,24368769,25265553,25850178

%N Numbers that are the sum of four fourth powers in six or more ways.

%H David Consiglio, Jr., <a href="/A344904/b344904.txt">Table of n, a(n) for n = 1..1000</a>

%e 3847554 is a term because 3847554 = 2^4 + 13^4 + 29^4 + 42^4 = 2^4 + 21^4 + 22^4 + 43^4 = 6^4 + 11^4 + 17^4 + 44^4 = 6^4 + 31^4 + 32^4 + 37^4 = 9^4 + 29^4 + 32^4 + 38^4 = 13^4 + 26^4 + 32^4 + 39^4.

%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, 1000)]

%o for pos in cwr(power_terms, 4):

%o tot = sum(pos)

%o keep[tot] += 1

%o rets = sorted([k for k, v in keep.items() if v >= 6])

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

%o print(rets[x])

%Y Cf. A344356, A344647, A344921, A344922, A344940, A345148.

%K nonn

%O 1,1

%A _David Consiglio, Jr._, Jun 02 2021