|
|
A256452
|
|
Number of integer solutions to n^2 = x^2 + y^2 with x>0, y>=0.
|
|
2
|
|
|
1, 1, 1, 1, 3, 1, 1, 1, 1, 3, 1, 1, 3, 1, 3, 1, 3, 1, 1, 3, 1, 1, 1, 1, 5, 3, 1, 1, 3, 3, 1, 1, 1, 3, 3, 1, 3, 1, 3, 3, 3, 1, 1, 1, 3, 1, 1, 1, 1, 5, 3, 3, 3, 1, 3, 1, 1, 3, 1, 3, 3, 1, 1, 1, 9, 1, 1, 3, 1, 3, 1, 1, 3, 3, 5, 1, 1, 3, 1, 3, 1, 3, 1, 1, 9, 1, 3
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,5
|
|
LINKS
|
|
|
FORMULA
|
Multiplicative with a(p^e) = 2*e + 1 if p == 1 (mod 4), otherwise a(p^e) = 1.
|
|
MATHEMATICA
|
a[ n_] := Sum[ Mod[ Length@Divisors[n^2 - k^2], 2], {k, n}];
a[ n_] := Length @ FindInstance[ n^2 == x^2 + y^2 && x > 0 && y >= 0, {x, y}, Integers, 10^9]; (* Michael Somos, Aug 15 2016 *)
f[p_, e_] := If[Mod[p, 4] == 1, 2*e + 1, 1]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Sep 12 2020 *)
|
|
PROG
|
(PARI) {a(n) = sum(k=1, n, issquare(n^2 - k^2))};
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,mult
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|