cp's OEIS Frontend

A345830 Numbers that are the sum of seven fourth powers in exactly eight ways.

%I A345830 #6 Jul 31 2021 21:37:00
%S A345830 21252,21507,21636,21876,25347,30372,31412,31652,32116,32356,33811,
%T A345830 33907,35637,35652,35892,36261,37827,38052,38596,38676,39267,39347,
%U A345830 39971,39972,40212,40452,41506,41731,41987,42147,42227,42357,42532,42771,42852,43027,43282
%N A345830 Numbers that are the sum of seven fourth powers in exactly eight ways.
%C A345830 Differs from A345574 at term 1 because 19491 = 1^4 + 1^4 + 1^4 + 6^4 + 8^4 + 8^4 + 10^4  = 1^4 + 2^4 + 4^4 + 4^4 + 7^4 + 9^4 + 10^4  = 1^4 + 2^4 + 5^4 + 8^4 + 8^4 + 8^4 + 9^4  = 1^4 + 3^4 + 4^4 + 6^4 + 6^4 + 9^4 + 10^4  = 2^4 + 2^4 + 2^4 + 3^4 + 5^4 + 8^4 + 11^4  = 2^4 + 4^4 + 4^4 + 5^4 + 6^4 + 7^4 + 11^4  = 3^4 + 4^4 + 4^4 + 7^4 + 7^4 + 8^4 + 10^4  = 3^4 + 4^4 + 5^4 + 6^4 + 6^4 + 6^4 + 11^4  = 3^4 + 5^4 + 7^4 + 8^4 + 8^4 + 8^4 + 8^4.
%H A345830 Sean A. Irvine, <a href="/A345830/b345830.txt">Table of n, a(n) for n = 1..10000</a>
%e A345830 21252 is a term because 21252 = 1^4 + 1^4 + 1^4 + 1^4 + 4^4 + 4^4 + 12^4 = 1^4 + 1^4 + 2^4 + 2^4 + 2^4 + 9^4 + 11^4 = 1^4 + 1^4 + 7^4 + 8^4 + 8^4 + 8^4 + 9^4 = 1^4 + 2^4 + 2^4 + 3^4 + 7^4 + 8^4 + 11^4 = 1^4 + 2^4 + 3^4 + 3^4 + 3^4 + 4^4 + 12^4 = 1^4 + 2^4 + 4^4 + 6^4 + 9^4 + 9^4 + 9^4 = 1^4 + 4^4 + 4^4 + 6^4 + 7^4 + 7^4 + 11^4 = 3^4 + 4^4 + 6^4 + 7^4 + 8^4 + 9^4 + 9^4.
%o A345830 (Python)
%o A345830 from itertools import combinations_with_replacement as cwr
%o A345830 from collections import defaultdict
%o A345830 keep = defaultdict(lambda: 0)
%o A345830 power_terms = [x**4 for x in range(1, 1000)]
%o A345830 for pos in cwr(power_terms, 7):
%o A345830     tot = sum(pos)
%o A345830     keep[tot] += 1
%o A345830     rets = sorted([k for k, v in keep.items() if v == 8])
%o A345830     for x in range(len(rets)):
%o A345830         print(rets[x])
%Y A345830 Cf. A345574, A345780, A345820, A345829, A345831, A345840, A346285.
%K A345830 nonn
%O A345830 1,1
%A A345830 _David Consiglio, Jr._, Jun 26 2021