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A345337 Numbers that are the sum of four fifth powers in three or more ways.

%I A345337 #12 Jul 31 2021 17:02:50
%S A345337 1479604544,8429250269,31738437018,47347345408,101802671905,
%T A345337 213625838382,269736008608,288202145792,353946845525,355891431456,
%U A345337 359543904192,434029382875,453675031150,467943544849,470899924000,476304861791,568433238331,690221638656,706199665600
%N A345337 Numbers that are the sum of four fifth powers in three or more ways.
%C A345337 No numbers that are the sum of four fifth powers in four ways have been found. As a result, there is no corresponding sequence for the sum of four fifth powers in exactly three ways.
%H A345337 Sean A. Irvine, <a href="/A345337/b345337.txt">Table of n, a(n) for n = 1..500</a>
%e A345337 8429250269 is a term because 8429250269 = 4^5 + 41^5 + 73^5 + 91^5  = 13^5 + 28^5 + 82^5 + 86^5  = 21^5 + 27^5 + 68^5 + 93^5.
%o A345337 (Python)
%o A345337 from itertools import combinations_with_replacement as cwr
%o A345337 from collections import defaultdict
%o A345337 keep = defaultdict(lambda: 0)
%o A345337 power_terms = [x**5 for x in range(1, 1000)]
%o A345337 for pos in cwr(power_terms, 4):
%o A345337     tot = sum(pos)
%o A345337     keep[tot] += 1
%o A345337 rets = sorted([k for k, v in keep.items() if v >= 3])
%o A345337 for x in range(len(rets)):
%o A345337     print(rets[x])
%Y A345337 Cf. A342687, A344241, A344644.
%K A345337 nonn
%O A345337 1,1
%A A345337 _David Consiglio, Jr._, Jun 14 2021