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A176197 Sum of 4 distinct nonzero fourth powers.

%I A176197 #4 May 17 2023 10:11:48
%S A176197 354,723,898,963,978,1394,1569,1634,1649,1938,2003,2018,2178,2193,
%T A176197 2258,2499,2674,2739,2754,3043,3108,3123,3283,3298,3363,3714,3779,
%U A176197 3794,3954,3969,4034,4194,4323,4338,4369,4403,4434,4449,4578,4738,4803,4818,4978
%N A176197 Sum of 4 distinct nonzero fourth powers.
%C A176197 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 A176197 <a href="http://www.sciencedaily.com/releases/2008/03/080314145039.htm">Part of "Euler's Equation of degree four"</a>
%p A176197 # returns number of ways of writing n as a^4+b^4+c^4+d^4, 1<=a<b<c<d.
%p A176197 A176197 := proc(n)
%p A176197     local a,i,j,k,l,res ;
%p A176197     a := 0 ;
%p A176197     for i from 1 do
%p A176197         if i^4 > n then
%p A176197             break ;
%p A176197         end if;
%p A176197         for j from i+1 do
%p A176197             if i^4+j^4 > n then
%p A176197                 break ;
%p A176197             end if;
%p A176197             for k from j+1 do
%p A176197                 if i^4+j^4+k^4> n then
%p A176197                     break;
%p A176197                 end if;
%p A176197                 res := n-i^4-j^4-k^4 ;
%p A176197                 if issqr(res) then
%p A176197                     res := sqrt(res) ;
%p A176197                     if issqr(res) then
%p A176197                         l := sqrt(res) ;
%p A176197                         if l > k then
%p A176197                             a := a+1 ;
%p A176197                         end if;
%p A176197                     end if;
%p A176197                 end if;
%p A176197             end do:
%p A176197         end do:
%p A176197     end do:
%p A176197     a ;
%p A176197 end proc:
%p A176197 for n from 1 do
%p A176197     if A176197(n) > 0 then
%p A176197         print(n) ;
%p A176197     end if;
%p A176197 end do: # _R. J. Mathar_, May 17 2023
%t A176197 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 A176197 Subsequence of A003338.
%K A176197 nonn
%O A176197 1,1
%A A176197 _Vladimir Joseph Stephan Orlovsky_, Apr 11 2010