cp's OEIS Frontend

A344519 Numbers that are the sum of five positive fifth powers in exactly four ways.

%I A344519 #10 Jan 11 2025 04:14:29
%S A344519 287618651,1386406515,1763135232,2494769760,2619898293,3096064443,
%T A344519 3291315732,3749564512,4045994624,5142310350,5183605813,5658934676,
%U A344519 5880926107,7205217018,7401155424,7691215599,8429499101,8926086432,9051501568,9203796832,9254212901
%N A344519 Numbers that are the sum of five positive fifth powers in exactly four ways.
%C A344519 Differs from A344518 at term 20 because
%C A344519 9006349824 =  8^5 + 34^5 + 62^5 + 68^5 + 92^5
%C A344519            =  8^5 + 41^5 + 47^5 + 79^5 + 89^5
%C A344519            = 12^5 + 18^5 + 72^5 + 78^5 + 84^5
%C A344519            = 21^5 + 34^5 + 43^5 + 74^5 + 92^5
%C A344519            = 24^5 + 42^5 + 48^5 + 54^5 + 96^5.
%H A344519 Sean A. Irvine, <a href="/A344519/b344519.txt">Table of n, a(n) for n = 1..4857</a>
%e A344519 287618651 is a term because
%e A344519 287618651 =  8^5 + 21^5 + 27^5 + 27^5 + 48^5
%e A344519           =  9^5 + 13^5 + 26^5 + 37^5 + 46^5
%e A344519           = 11^5 + 12^5 + 23^5 + 41^5 + 44^5
%e A344519           = 11^5 + 20^5 + 22^5 + 30^5 + 48^5.
%e A344519 [Corrected by _Patrick De Geest_, Dec 28 2024]
%o A344519 (Python)
%o A344519 from itertools import combinations_with_replacement as cwr
%o A344519 from collections import defaultdict
%o A344519 keep = defaultdict(lambda: 0)
%o A344519 power_terms = [x**5 for x in range(1, 500)]
%o A344519 for pos in cwr(power_terms, 5):
%o A344519     tot = sum(pos)
%o A344519     keep[tot] += 1
%o A344519 rets = sorted([k for k, v in keep.items() if v == 4])
%o A344519 for x in range(len(rets)):
%o A344519     print(rets[x])
%Y A344519 Cf. A003350, A004845, A342685, A342686, A342687, A342688, A344244, A344355, A344518, A345863, A345864, A346257, A346358, A346359.
%K A344519 nonn
%O A344519 1,1
%A A344519 _David Consiglio, Jr._, May 21 2021