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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.
a(n) = 1 + 2*A046080(n) if n>0.
a(n) = A046109(n)/4 for n > 0. - Hugo Pfoertner, Sep 21 2023
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
Sequence in context: A350559 A365401 A212181 * A330827 A010276 A214268
KEYWORD
nonn,mult
AUTHOR
Michael Somos, Mar 29 2015
STATUS
approved

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Last modified February 26 02:20 EST 2024. Contains 370335 sequences. (Running on oeis4.)