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.
%I A378880 #12 Jun 09 2025 09:03:18
%S A378880 0,1,1,2,-1,2,1,3,2,0,1,3,-1,2,0,4,-1,3,1,1,2,2,1,4,-2,0,3,3,-1,1,1,5,
%T A378880 2,0,0,4,-1,2,0,2,-1,3,1,3,1,2,1,5,2,-1,0,1,-1,4,0,4,2,0,1,2,-1,2,3,6,
%U A378880 -2,3,1,1,2,1,1,5,-1,0,-1,3,2,1,1,3,4,0
%N A378880 a(n) = A378879(n) - A083025(n).
%F A378880 Totally additive with a(p) = 1 if p = 2 or p == 3 (mod 4), and a(p) = -1 if p == 1 (mod 4). - _Amiram Eldar_, Jun 09 2025
%e A378880 a(10) = 0 because the factorization 2*5 has 1 each of a Pythagorean prime, 5, and a non-Pythagorean prime, 2.
%t A378880 f[{x_, y_}] := If[Mod[x, 4] == 1, y, -y];
%t A378880 s[n_] := Map[f, FactorInteger[n]];
%t A378880 p[n_] := {Total[Select[s[n], # > 0 &]], -Total[Select[s[n], # < 0 &]]};
%t A378880 p[1] = {0, 0};
%t A378880 t = Table[p[n], {n, 1, 135}]
%t A378880 u = Map[First, t] (* A083025 *)
%t A378880 v = Map[Last, t] (* A378879 *)
%t A378880 v - u (* A377625 *)
%Y A378880 Cf. A000040, A002144, A002145, A083025, A378879.
%K A378880 sign,easy
%O A378880 1,4
%A A378880 _Clark Kimberling_, Jan 14 2025