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A379398 Numbers that can be written in exactly three different ways as a sum of at most nine positive third powers.

%I A379398 #12 Dec 26 2024 20:06:02
%S A379398 35,56,64,65,67,68,70,75,81,82,83,84,86,89,92,93,94,96,97,98,99,100,
%T A379398 105,107,108,110,112,113,118,119,120,121,124,125,127,130,141,142,143,
%U A379398 148,149,150,151,167,169,174,175,176,177,178,183,186,188,202,204,212,213,214,240,247,303
%N A379398 Numbers that can be written in exactly three different ways as a sum of at most nine positive third powers.
%C A379398 The 'nine' is not arbitrary. Waring stated that every natural number can be expressed as a sum of at most nine cubes. (Cf. A002804)
%H A379398 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/WaringsProblem.html">Waring's Problem</a>
%H A379398 Wikipedia, <a href="https://en.wikipedia.org/wiki/Waring%27s_problem">Waring's Problem</a>
%H A379398 <a href="/index/Su#ssq">Index entries for sequences related to sums of cubes</a>
%e A379398 67 is in the sequence since 1^3+1^3+1^3+4^3 = 2^3+2^3+2^3+2^3+2^3+3^3 = 1^3+1^3+1^3+1^3+1^3+2^3+3^3+3^3.
%o A379398 (PARI) upto(n) = my(v=vector(n), maxb=sqrtnint(n,3)); forvec(x=vector(9,i,[0,maxb]), s=sum(i=1,9,x[i]^3); if(0<s && s<=n, v[s]++); , 1); Vec(select(x->x==3,v,1)) \\ _David A. Corneth_, Dec 23 2024
%Y A379398 Cf. A002804, A025453, A379396, A379397, A379399, A379400
%K A379398 nonn
%O A379398 1,1
%A A379398 _Patrick De Geest_, Dec 22 2024