A176197 Sum of 4 distinct nonzero fourth powers.

354, 723, 898, 963, 978, 1394, 1569, 1634, 1649, 1938, 2003, 2018, 2178, 2193, 2258, 2499, 2674, 2739, 2754, 3043, 3108, 3123, 3283, 3298, 3363, 3714, 3779, 3794, 3954, 3969, 4034, 4194, 4323, 4338, 4369, 4403, 4434, 4449, 4578, 4738, 4803, 4818, 4978

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Apr 11 2010

Keywords

• nonn

Comments

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,..

Links

• Part of "Euler's Equation of degree four"

Crossrefs

Subsequence of A003338.

Programs

Maple

# returns number of ways of writing n as a^4+b^4+c^4+d^4, 1<=aA176197 := proc(n)
    local a,i,j,k,l,res ;
    a := 0 ;
    for i from 1 do
        if i^4 > n then
            break ;
        end if;
        for j from i+1 do
            if i^4+j^4 > n then
                break ;
            end if;
            for k from j+1 do
                if i^4+j^4+k^4> n then
                    break;
                end if;
                res := n-i^4-j^4-k^4 ;
                if issqr(res) then
                    res := sqrt(res) ;
                    if issqr(res) then
                        l := sqrt(res) ;
                        if l > k then
                            a := a+1 ;
                        end if;
                    end if;
                end if;
            end do:
        end do:
    end do:
    a ;
end proc:
for n from 1 do
    if A176197(n) > 0 then
        print(n) ;
    end if;
end do: # R. J. Mathar, May 17 2023

Mathematica

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