A345862 - OEIS

%I #6 Jul 31 2021 20:00:36

%S 6885,7990,8035,8165,8275,8340,8515,8565,8580,9140,9235,9285,9445,

%T 9495,9510,9540,9620,9670,9795,9830,9860,9924,9925,9990,10005,10164,

%U 10294,10340,10374,10404,10420,10515,10534,10884,10950,10980,11075,11125,11190,11220

%N Numbers that are the sum of ten fourth powers in exactly ten ways.

%C Differs from A345603 at term 4 because 8100 = 1^4 + 1^4 + 1^4 + 2^4 + 2^4 + 2^4 + 4^4 + 6^4 + 7^4 + 8^4  = 1^4 + 1^4 + 1^4 + 2^4 + 2^4 + 3^4 + 6^4 + 6^4 + 6^4 + 8^4  = 1^4 + 1^4 + 1^4 + 4^4 + 4^4 + 4^4 + 4^4 + 4^4 + 4^4 + 9^4  = 1^4 + 1^4 + 1^4 + 4^4 + 4^4 + 6^4 + 6^4 + 6^4 + 6^4 + 7^4  = 1^4 + 2^4 + 2^4 + 2^4 + 2^4 + 2^4 + 3^4 + 3^4 + 6^4 + 9^4  = 2^4 + 2^4 + 2^4 + 2^4 + 3^4 + 3^4 + 3^4 + 6^4 + 7^4 + 8^4  = 2^4 + 2^4 + 2^4 + 3^4 + 4^4 + 4^4 + 4^4 + 7^4 + 7^4 + 7^4  = 2^4 + 2^4 + 3^4 + 3^4 + 4^4 + 4^4 + 6^4 + 6^4 + 7^4 + 7^4  = 2^4 + 3^4 + 3^4 + 3^4 + 4^4 + 4^4 + 4^4 + 4^4 + 4^4 + 9^4  = 2^4 + 3^4 + 3^4 + 3^4 + 4^4 + 6^4 + 6^4 + 6^4 + 6^4 + 7^4  = 3^4 + 3^4 + 3^4 + 3^4 + 6^4 + 6^4 + 6^4 + 6^4 + 6^4 + 6^4.

%H Sean A. Irvine, <a href="/A345862/b345862.txt">Table of n, a(n) for n = 1..10000</a>

%e 7990 is a term because 7990 = 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 6^4 + 6^4 + 6^4 + 8^4 = 1^4 + 1^4 + 1^4 + 1^4 + 2^4 + 2^4 + 2^4 + 3^4 + 6^4 + 9^4 = 1^4 + 1^4 + 1^4 + 2^4 + 2^4 + 3^4 + 3^4 + 6^4 + 7^4 + 8^4 = 1^4 + 1^4 + 1^4 + 2^4 + 4^4 + 4^4 + 4^4 + 7^4 + 7^4 + 7^4 = 1^4 + 1^4 + 1^4 + 3^4 + 4^4 + 4^4 + 6^4 + 6^4 + 7^4 + 7^4 = 1^4 + 4^4 + 4^4 + 4^4 + 5^4 + 5^4 + 5^4 + 5^4 + 5^4 + 8^4 = 2^4 + 2^4 + 3^4 + 3^4 + 3^4 + 4^4 + 4^4 + 7^4 + 7^4 + 7^4 = 2^4 + 3^4 + 3^4 + 3^4 + 3^4 + 4^4 + 6^4 + 6^4 + 7^4 + 7^4 = 3^4 + 3^4 + 3^4 + 3^4 + 3^4 + 4^4 + 4^4 + 4^4 + 4^4 + 9^4 = 3^4 + 3^4 + 3^4 + 3^4 + 3^4 + 6^4 + 6^4 + 6^4 + 6^4 + 7^4.

%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, 10):

%o     tot = sum(pos)

%o     keep[tot] += 1

%o     rets = sorted([k for k, v in keep.items() if v == 10])

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

%o         print(rets[x])

%Y Cf. A345603, A345812, A345852, A345861, A346355.

%K nonn

%O 1,1

%A _David Consiglio, Jr._, Jun 26 2021