This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
a(2) = 40 because 40*41 / 2 = 820 = 6^2 + 28^2 = 12^2 + 26^2.
a(11) = 3 as A336542 = 325 and can be written in three ways as a sum of two nonzero squares.
2^5 = 32 = 4^2 + 4^2. So a(2) = 1. 5^5 = 3125 = 10^2 + 55^2 = 25^2 + 50^2 = 38^2 + 41^2. So a(5) = 3.
f:= proc(n) local x,y,S;
S:= map(t -> subs(t,[x,y]),[isolve(x^2+y^2=n^5)]);
nops(select(t -> t[1] >= t[2] and t[2] > 0, S))
end proc:
map(f, [$0..200]); # Robert Israel, Mar 03 2021
a(n) = my(cnt=0, m=n^5); for(k=1, sqrt(m/2), l=m-k*k; if(l>0&&issquare(l), cnt++)); cnt;
a(2) = 25 because 25*2 = 50 is the least even number that is the sum of two nonzero squares in exactly 2 ways; 50 = 1^2 + 7^2 = 5^2 + 5^2.
nR[n_] := (SquaresR[2, n] + Plus @@ Pick[{-4, 4}, IntegerQ /@ Sqrt[{n, n/2}]])/8; a[n_] := Block[{k=1}, While[nR[n * k] != n, k++]; k]; Array[a, 10] (* Giovanni Resta, May 27 2016 *)
a(2) = 6 from 6^2 + 7^2 = 2^2 + 9^2. a(3) = 21 from 21^2 + 22^2 = 5^2 + 30^2 = 14^2 + 27^2. a(4) = 23 form 23^2 + 24^2 = 4^2 + 33^2 = 9^2 + 32^2 = 12^2 + 31^2.
A025426(n)=my(v=valuation(n, 2), f=factor(n>>v), t=1); for(i=1, #f~, if(f[i, 1]%4>1, if(f[i, 2]%2, return(0)), t*=f[i, 2]+1)); if(t%2, t-(-1)^v, t)/2 a(n)=my(k=1); while(A025426(2*k*(k+1)+1)!=n, k++); k \\ Charles R Greathouse IV, Jun 03 2016
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