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A047721 Sum of 10 but no fewer nonzero fourth powers.

%I A047721 #13 Oct 25 2021 08:07:35
%S A047721 10,25,40,55,70,90,105,120,135,150,160,170,185,200,215,225,230,250,
%T A047721 265,280,295,310,330,345,360,375,390,400,410,425,440,455,465,470,485,
%U A047721 490,505,520,535,550,565,570,585,600,615,634,640,650,665,680,695,714,730
%N A047721 Sum of 10 but no fewer nonzero fourth powers.
%H A047721 David A. Corneth, <a href="/A047721/b047721.txt">Table of n, a(n) for n = 1..15256</a>
%o A047721 (PARI) upto(n)={my(e=10); my(s=sum(k=1, sqrtint(sqrtint(n)), x^(k^4)) + O(x*x^n)); my(p=s^e, q=(1 + s)^(e-1)); select(k->polcoeff(p,k) && !polcoeff(q,k), [1..n])} \\ _Andrew Howroyd_, Jul 06 2018
%o A047721 (Python)
%o A047721 from itertools import count, takewhile, combinations_with_replacement as mc
%o A047721 def aupto(lim):
%o A047721     p4 = list(takewhile(lambda x: x <= lim, (i**4 for i in count(1))))
%o A047721     s = [set(sum(c) for c in mc(p4, i) if sum(c) <= lim) for i in range(11)]
%o A047721     ans = s[10]
%o A047721     for i in range(1, 10):
%o A047721         ans -= s[i]
%o A047721     return sorted(ans)
%o A047721 print(aupto(730)) # _Michael S. Branicky_, Oct 25 2021
%Y A047721 Cf. A000583, A002377, A003344, A047720, A047722, A047723.
%K A047721 nonn
%O A047721 1,1
%A A047721 Arlin Anderson (starship1(AT)gmail.com)