A346330 - OEIS

%I #6 Jul 31 2021 19:03:52

%S 926372,952653,993573,1133343,1414591,1431366,1447327,1597928,1637020,

%T 1663391,1697685,1876624,1933329,1992377,1993376,1993666,2033328,

%U 2091879,2175912,2182160,2231110,2280544,2280575,2280786,2281567,2283668,2329602,2345563,2388619

%N Numbers that are the sum of eight fifth powers in exactly five ways.

%C Differs from A345613 at term 7 because 1431397 = 3^5 + 5^5 + 6^5 + 7^5 + 8^5 + 11^5 + 11^5 + 16^5 = 1^5 + 5^5 + 8^5 + 8^5 + 8^5 + 8^5 + 14^5 + 15^5 = 3^5 + 3^5 + 3^5 + 10^5 + 10^5 + 10^5 + 13^5 + 15^5 = 2^5 + 2^5 + 4^5 + 10^5 + 11^5 + 11^5 + 12^5 + 15^5 = 1^5 + 2^5 + 7^5 + 7^5 + 11^5 + 11^5 + 14^5 + 14^5 = 1^5 + 2^5 + 6^5 + 7^5 + 12^5 + 12^5 + 13^5 + 14^5.

%H Sean A. Irvine, <a href="/A346330/b346330.txt">Table of n, a(n) for n = 1..10000</a>

%e 926372 is a term because 926372 = 5^5 + 6^5 + 6^5 + 6^5 + 6^5 + 8^5 + 10^5 + 15^5 = 4^5 + 6^5 + 6^5 + 7^5 + 7^5 + 7^5 + 10^5 + 15^5 = 2^5 + 5^5 + 8^5 + 8^5 + 8^5 + 8^5 + 8^5 + 15^5 = 2^5 + 2^5 + 7^5 + 7^5 + 8^5 + 11^5 + 11^5 + 14^5 = 2^5 + 2^5 + 6^5 + 7^5 + 8^5 + 12^5 + 12^5 + 13^5.

%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, 8):

%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. A345613, A345837, A346282, A346329, A346331, A346340.

%K nonn

%O 1,1

%A _David Consiglio, Jr._, Jul 13 2021