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 A382331 #13 Mar 29 2025 18:55:10
%S A382331 0,2,3,-2,5,5,7,2,-3,7,11,1,13,9,8,-2,17,-1,19,3,10,13,23,5,-5,15,3,5,
%T A382331 29,10,31,2,14,19,12,-5,37,21,16,7,41,12,43,9,2,25,47,1,-7,-3,20,11,
%U A382331 53,5,16,9,22,31,59,6,61,33,4,-2,18,16,67,15,26,14,71,-1,73,39,-2
%N A382331 If n = Product (p_j^k_j) then a(n) = -Sum ((-1)^k_j * p_j).
%H A382331 <a href="/index/Eu#epf">Index entries for sequences computed from exponents in factorization of n</a>.
%H A382331 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>.
%F A382331 Additive with a(p^e) = (-1)^(e+1) * p.
%e A382331 a(72) = a(2^3*3^2) = 2 - 3 = -1.
%t A382331 Join[{0}, Table[-Plus @@ ((-1)^#[[2]] #[[1]] & /@ FactorInteger[n]), {n, 2, 75}]]
%o A382331 (PARI) a(n) = my(f=factor(n)); -sum(i=1, #f~, (-1)^f[i,2]*f[i,1]); \\ _Michel Marcus_, Mar 22 2025
%Y A382331 Cf. A001414, A008472, A316523, A332422, A332423, A332424, A340901, A366749.
%K A382331 sign,easy
%O A382331 1,2
%A A382331 _Ilya Gutkovskiy_, Mar 22 2025