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%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
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