%I #10 Mar 13 2023 10:20:42
%S 1,5,10,10,6,5,6,4,2,5,10,10,6,4,3,1,2,9,15,11,4,3,3,1,2,8,13,12,10,9,
%T 5,2,5,12,15,9,5,10,12,6,3,7,10,9,10,11,6,2,4,10,14,10,8,11,8,2,2,7,
%U 10,9,9,7,2,2,9,21,26,16,9,13,11,3,3,11,16,12,9,9,5,3,8,21,29,21,14,12,7,3,4
%N Number of 5tuples (x,y,z,t,u) of nonnegative integers such that x^2+y^3+z^4+t^5+u^6 = n.
%C a(n) > 0 for n <= 10000. Is there any n for which a(n) = 0?
%C Note that there are many famous hard problems connected with sequences A045634, A135910, A135911 and the present entry (see the Ford reference).
%C The graph of this sequence suggests that a(n) is never zero. Checked to 10^5.  _T. D. Noe_, Mar 07 2008
%H T. D. Noe, <a href="/A135912/b135912.txt">Table of n, a(n) for n = 0..10000</a>
%H K. B. Ford, <a href="https://doi.org/10.1090/S0894034796001932">The representation of numbers as sums of unlike powers II</a>, J. Amer. Math. Soc., 9 (1996), 919940.
%p M:=100; M2:=M^2; t0:=array(0..M2); for i from 0 to M2 do t0[i]:=0; od:
%p for a from 0 to M do na:=a^2; for b from 0 to M do nb:=na+b^3;
%p if nb <= M2 then for c from 0 to M do nc:=nb+c^4; if nc <= M2 then for d from 0 to M2 do nd:=nc+d^5; if nd <= M2 then for e from 0 to M2 do i:=nd+e^6; if i <= M2 then t0[i]:=t0[i]+1; fi; od: fi; od; fi; od: fi; od: od:
%p [seq(t0[i],i=0..M2)];
%p for i from 0 to M2 do if t0[i]=0 then lprint(i); fi; od:
%Y Cf. A045634, A135910, A135911.
%K nonn
%O 0,2
%A _N. J. A. Sloane_, Mar 07 2008
