A345337 - OEIS

%I #12 Jul 31 2021 17:02:50

%S 1479604544,8429250269,31738437018,47347345408,101802671905,

%T 213625838382,269736008608,288202145792,353946845525,355891431456,

%U 359543904192,434029382875,453675031150,467943544849,470899924000,476304861791,568433238331,690221638656,706199665600

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

%C 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 Sean A. Irvine, <a href="/A345337/b345337.txt">Table of n, a(n) for n = 1..500</a>

%e 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 (Python)

%o from itertools import combinations_with_replacement as cwr

%o from collections import defaultdict

%o keep = defaultdict(lambda: 0)

%o power_terms = [x**5 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 >= 3])

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

%o     print(rets[x])

%Y Cf. A342687, A344241, A344644.

%K nonn

%O 1,1

%A _David Consiglio, Jr._, Jun 14 2021