cp's OEIS Frontend

A345852 Numbers that are the sum of nine fourth powers in exactly ten ways.

%I A345852 #6 Jul 31 2021 21:28:42
%S A345852 9299,12708,12948,13269,13349,13524,13589,13764,13829,13893,14133,
%T A345852 14228,14468,14564,14869,14934,14964,15014,15094,15109,15174,15189,
%U A345852 15333,15428,15429,15524,15588,15604,15653,16214,16229,16469,16564,16644,16773,16883,16948
%N A345852 Numbers that are the sum of nine fourth powers in exactly ten ways.
%C A345852 Differs from A345594 at term 15 because 14804 = 1^4 + 1^4 + 1^4 + 2^4 + 2^4 + 2^4 + 8^4 + 8^4 + 9^4  = 1^4 + 1^4 + 1^4 + 4^4 + 6^4 + 6^4 + 6^4 + 8^4 + 9^4  = 1^4 + 1^4 + 2^4 + 2^4 + 2^4 + 2^4 + 2^4 + 3^4 + 11^4  = 1^4 + 1^4 + 2^4 + 2^4 + 3^4 + 7^4 + 8^4 + 8^4 + 8^4  = 1^4 + 1^4 + 4^4 + 4^4 + 6^4 + 7^4 + 7^4 + 8^4 + 8^4  = 1^4 + 2^4 + 2^4 + 2^4 + 3^4 + 4^4 + 6^4 + 9^4 + 9^4  = 2^4 + 2^4 + 3^4 + 3^4 + 4^4 + 6^4 + 7^4 + 8^4 + 9^4  = 2^4 + 3^4 + 3^4 + 3^4 + 6^4 + 6^4 + 6^4 + 8^4 + 9^4  = 2^4 + 4^4 + 4^4 + 4^4 + 4^4 + 7^4 + 7^4 + 7^4 + 9^4  = 2^4 + 6^4 + 6^4 + 6^4 + 6^4 + 7^4 + 7^4 + 7^4 + 7^4  = 3^4 + 4^4 + 4^4 + 4^4 + 6^4 + 6^4 + 7^4 + 7^4 + 9^4.
%H A345852 Sean A. Irvine, <a href="/A345852/b345852.txt">Table of n, a(n) for n = 1..10000</a>
%e A345852 12708 is a term because 12708 = 1^4 + 1^4 + 1^4 + 2^4 + 2^4 + 2^4 + 4^4 + 7^4 + 10^4 = 1^4 + 1^4 + 1^4 + 2^4 + 2^4 + 3^4 + 6^4 + 6^4 + 10^4 = 1^4 + 1^4 + 1^4 + 5^4 + 6^4 + 6^4 + 6^4 + 8^4 + 8^4 = 1^4 + 2^4 + 2^4 + 2^4 + 3^4 + 5^4 + 6^4 + 8^4 + 9^4 = 1^4 + 2^4 + 4^4 + 4^4 + 5^4 + 6^4 + 6^4 + 7^4 + 9^4 = 1^4 + 3^4 + 4^4 + 5^4 + 6^4 + 6^4 + 6^4 + 6^4 + 9^4 = 2^4 + 2^4 + 2^4 + 2^4 + 3^4 + 3^4 + 3^4 + 7^4 + 10^4 = 2^4 + 2^4 + 3^4 + 3^4 + 5^4 + 6^4 + 7^4 + 8^4 + 8^4 = 2^4 + 4^4 + 4^4 + 4^4 + 5^4 + 7^4 + 7^4 + 7^4 + 8^4 = 3^4 + 4^4 + 4^4 + 5^4 + 6^4 + 6^4 + 7^4 + 7^4 + 8^4.
%o A345852 (Python)
%o A345852 from itertools import combinations_with_replacement as cwr
%o A345852 from collections import defaultdict
%o A345852 keep = defaultdict(lambda: 0)
%o A345852 power_terms = [x**4 for x in range(1, 1000)]
%o A345852 for pos in cwr(power_terms, 9):
%o A345852     tot = sum(pos)
%o A345852     keep[tot] += 1
%o A345852     rets = sorted([k for k, v in keep.items() if v == 10])
%o A345852     for x in range(len(rets)):
%o A345852         print(rets[x])
%Y A345852 Cf. A345594, A345802, A345842, A345851, A345862, A346345.
%K A345852 nonn
%O A345852 1,1
%A A345852 _David Consiglio, Jr._, Jun 26 2021