The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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. 4

%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 5-tuples (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/S0894-0347-96-00193-2">The representation of numbers as sums of unlike powers II</a>, J. Amer. Math. Soc., 9 (1996), 919-940.

%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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified September 8 10:03 EDT 2024. Contains 375753 sequences. (Running on oeis4.)