A135912 Number of 5-tuples (x,y,z,t,u) of nonnegative integers such that x^2+y^3+z^4+t^5+u^6 = n.

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, 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, 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

Offset: 0

Author

N. J. A. Sloane, Mar 07 2008

Keywords

• nonn

Comments

a(n) > 0 for n <= 10000. Is there any n for which a(n) = 0?

Note that there are many famous hard problems connected with sequences A045634, A135910, A135911 and the present entry (see the Ford reference).

The graph of this sequence suggests that a(n) is never zero. Checked to 10^5. - T. D. Noe, Mar 07 2008

Links

• T. D. Noe, Table of n, a(n) for n = 0..10000
• K. B. Ford, The representation of numbers as sums of unlike powers II, J. Amer. Math. Soc., 9 (1996), 919-940.

Crossrefs

Cf. A045634, A135910, A135911.

Programs

Maple

M:=100; M2:=M^2; t0:=array(0..M2); for i from 0 to M2 do t0[i]:=0; od:
for a from 0 to M do na:=a^2; for b from 0 to M do nb:=na+b^3;
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:
[seq(t0[i],i=0..M2)];
for i from 0 to M2 do if t0[i]=0 then lprint(i); fi; od: