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,..
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
KEYWORD
nonn
AUTHOR
Vladimir Joseph Stephan Orlovsky, Apr 11 2010
STATUS
approved