A176197 - OEIS

%I #4 May 17 2023 10:11:48

%S 354,723,898,963,978,1394,1569,1634,1649,1938,2003,2018,2178,2193,

%T 2258,2499,2674,2739,2754,3043,3108,3123,3283,3298,3363,3714,3779,

%U 3794,3954,3969,4034,4194,4323,4338,4369,4403,4434,4449,4578,4738,4803,4818,4978

%N Sum of 4 distinct nonzero fourth powers.

%C 1^4+2^4+3^4+4^4=354, 1^4+2^4+3^4+5^4=723, .., 2^4+3^4+4^4+5^4=978,..

%H <a href="http://www.sciencedaily.com/releases/2008/03/080314145039.htm">Part of "Euler's Equation of degree four"</a>

%p # returns number of ways of writing n as a^4+b^4+c^4+d^4, 1<=a<b<c<d.

%p A176197 := proc(n)

%p     local a,i,j,k,l,res ;

%p     a := 0 ;

%p     for i from 1 do

%p         if i^4 > n then

%p             break ;

%p         end if;

%p         for j from i+1 do

%p             if i^4+j^4 > n then

%p                 break ;

%p             end if;

%p             for k from j+1 do

%p                 if i^4+j^4+k^4> n then

%p                     break;

%p                 end if;

%p                 res := n-i^4-j^4-k^4 ;

%p                 if issqr(res) then

%p                     res := sqrt(res) ;

%p                     if issqr(res) then

%p                         l := sqrt(res) ;

%p                         if l > k then

%p                             a := a+1 ;

%p                         end if;

%p                     end if;

%p                 end if;

%p             end do:

%p         end do:

%p     end do:

%p     a ;

%p end proc:

%p for n from 1 do

%p     if A176197(n) > 0 then

%p         print(n) ;

%p     end if;

%p end do: # _R. J. Mathar_, May 17 2023

%t lst={};Do[Do[Do[Do[AppendTo[lst,a^4+b^4+c^4+d^4],{d,c+1,11}],{c,b+1,10}],{b,a+1,9}],{a,1,8}];Sort@lst

%Y Subsequence of A003338.

%K nonn

%O 1,1

%A _Vladimir Joseph Stephan Orlovsky_, Apr 11 2010