cp's OEIS Frontend

A342688 Numbers that are the sum of five positive fifth powers in exactly three ways.

%I A342688 #21 Jan 11 2025 04:13:45
%S A342688 13124675,28055699,50043937,52679923,53069024,55097976,57936559,
%T A342688 60484744,62260463,62445305,70211956,73133026,79401728,80368962,
%U A342688 84766210,88512249,93288865,98824300,106993391,113055482,117173891,120968132,123383875,126416258,131106051,131529588,132022925
%N A342688 Numbers that are the sum of five positive fifth powers in exactly three ways.
%C A342688 Differs from A342687:
%C A342688 287618651 =  8^5 + 21^5 + 27^5 + 27^5 + 48^5
%C A342688           =  9^5 + 13^5 + 26^5 + 37^5 + 46^5
%C A342688           = 11^5 + 12^5 + 23^5 + 41^5 + 44^5
%C A342688           = 11^5 + 20^5 + 22^5 + 30^5 + 48^5.
%C A342688 So 287618651 is a term of A342687 but not a term of this sequence.
%C A342688 [Corrected by _Patrick De Geest_, Dec 28 2024]
%H A342688 David Consiglio, Jr., <a href="/A342688/b342688.txt">Table of n, a(n) for n = 1..1000</a>
%e A342688 50043937 =  6^5 + 16^5 + 18^5 + 24^5 + 33^5
%e A342688          =  7^5 + 13^5 + 21^5 + 23^5 + 33^5
%e A342688          = 11^5 + 13^5 + 13^5 + 29^5 + 31^5
%e A342688 so 50043937 is a term of this sequence.
%e A342688 [Corrected by _Patrick De Geest_, Dec 28 2024]
%o A342688 (Python)
%o A342688 from itertools import combinations_with_replacement as cwr
%o A342688 from collections import defaultdict
%o A342688 keep = defaultdict(lambda: 0)
%o A342688 power_terms = [x**5 for x in range(1, 500)]
%o A342688 for pos in cwr(power_terms, 5):
%o A342688     tot = sum(pos)
%o A342688     keep[tot] += 1
%o A342688 rets = sorted([k for k, v in keep.items() if v == 3])
%o A342688 for x in range(len(rets)):
%o A342688     print(rets[x])
%Y A342688 Cf. A003350, A004845, A342685, A342686, A342687, A344244, A344519, A344518, A345863, A345864, A346257, A346358.
%K A342688 nonn
%O A342688 1,1
%A A342688 _David Consiglio, Jr._, May 18 2021