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A374012 Least number of 6th powers needed to represent n.

%I A374012 #25 Feb 16 2025 08:34:06
%S A374012 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,
%T A374012 27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,
%U A374012 50,51,52,53,54,55,56,57,58,59,60,61,62,63,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16
%N A374012 Least number of 6th powers needed to represent n.
%C A374012 a(703) = 73.
%D A374012 Pillai, S. S. (1940) On Waring’s problem g(6) = 73. Proc. Indian Acad. Sci. 12A: 30-40
%H A374012 Seiichi Manyama, <a href="/A374012/b374012.txt">Table of n, a(n) for n = 1..10000</a>
%H A374012 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/WaringsProblem.html">Waring's Problem</a>.
%F A374012 a(n) <= 73.
%o A374012 (PARI) a_vector(n, k=6) = my(v=vector(n), cnt=0, d=0, p=1, s=sum(j=1, sqrtnint(n, k), x^j^k)+x*O(x^n)); while(cnt<n, d++; p*=s; for(i=1, n, if(!v[i] && polcoef(p, i), v[i]=d; cnt++))); v;
%o A374012 (Python)
%o A374012 from itertools import count
%o A374012 from sympy.solvers.diophantine.diophantine import power_representation
%o A374012 def A374012(n):
%o A374012     if n == 1: return 1
%o A374012     for k in count(1):
%o A374012         try:
%o A374012             next(power_representation(n,6,k))
%o A374012         except:
%o A374012             continue
%o A374012         return k # _Chai Wah Wu_, Jun 25 2024
%Y A374012 Cf. A002828, A002376, A002377, A188462.
%Y A374012 Cf. A002804, A018886.
%K A374012 nonn,look
%O A374012 1,2
%A A374012 _Seiichi Manyama_, Jun 25 2024