cp's OEIS Frontend

A345846 Numbers that are the sum of nine fourth powers in exactly four ways.

%I A345846 #6 Jul 31 2021 21:28:22
%S A345846 2854,2919,2934,2949,2964,3014,3029,3094,3159,3174,3204,3254,3269,
%T A345846 3429,3444,3558,3573,3638,3798,3813,3974,4034,4134,4164,4179,4182,
%U A345846 4209,4214,4274,4294,4389,4439,4454,4534,4614,4644,4709,4773,4788,4838,4884,4918,4949
%N A345846 Numbers that are the sum of nine fourth powers in exactly four ways.
%C A345846 Differs from A345588 at term 11 because 3189 = 1^4 + 1^4 + 1^4 + 1^4 + 2^4 + 4^4 + 4^4 + 4^4 + 7^4  = 1^4 + 1^4 + 1^4 + 1^4 + 3^4 + 4^4 + 4^4 + 6^4 + 6^4  = 1^4 + 2^4 + 2^4 + 3^4 + 3^4 + 3^4 + 4^4 + 4^4 + 7^4  = 1^4 + 2^4 + 3^4 + 3^4 + 3^4 + 3^4 + 4^4 + 6^4 + 6^4  = 2^4 + 2^4 + 2^4 + 2^4 + 5^4 + 5^4 + 5^4 + 5^4 + 5^4.
%H A345846 Sean A. Irvine, <a href="/A345846/b345846.txt">Table of n, a(n) for n = 1..10000</a>
%e A345846 2919 is a term because 2919 = 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 4^4 + 4^4 + 7^4 = 1^4 + 1^4 + 1^4 + 2^4 + 3^4 + 3^4 + 3^4 + 4^4 + 7^4 = 1^4 + 1^4 + 1^4 + 3^4 + 3^4 + 3^4 + 3^4 + 6^4 + 6^4 = 2^4 + 2^4 + 3^4 + 3^4 + 3^4 + 3^4 + 3^4 + 3^4 + 7^4.
%o A345846 (Python)
%o A345846 from itertools import combinations_with_replacement as cwr
%o A345846 from collections import defaultdict
%o A345846 keep = defaultdict(lambda: 0)
%o A345846 power_terms = [x**4 for x in range(1, 1000)]
%o A345846 for pos in cwr(power_terms, 9):
%o A345846     tot = sum(pos)
%o A345846     keep[tot] += 1
%o A345846     rets = sorted([k for k, v in keep.items() if v == 4])
%o A345846     for x in range(len(rets)):
%o A345846         print(rets[x])
%Y A345846 Cf. A345588, A345796, A345836, A345845, A345847, A345856, A346339.
%K A345846 nonn
%O A345846 1,1
%A A345846 _David Consiglio, Jr._, Jun 26 2021