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

1,1

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

Table of n, a(n) for n=1..43.

Part of "Euler's Equation of degree four"

Maple

# returns number of ways of writing n as a^4+b^4+c^4+d^4, 1<=a<b<c<d.
A176197 := 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

Crossrefs

Subsequence of A003338.

Sequence in context: A068684 A270782 A251127 * A157668 A374696 A250157

Adjacent sequences: A176194 A176195 A176196 * A176198 A176199 A176200

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Apr 11 2010

Status

approved