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 A370896 #7 Mar 05 2024 11:52:10
%S A370896 1,-1,2,0,5,-1,6,4,7,-3,8,2,15,1,16,14,31,25,44,34,55,33,56,50,55,29,
%T A370896 32,18,47,17,48,46,79,45,80,74,111,73,112,102,143,101,144,122,137,91,
%U A370896 138,132,139,129,180,154,207,201,256,242,299,241,300,270,331,269
%N A370896 Partial alternating sums of the squarefree kernel function (A007947).
%H A370896 Amiram Eldar, <a href="/A370896/b370896.txt">Table of n, a(n) for n = 1..10000</a>
%H A370896 László Tóth, <a href="https://www.emis.de/journals/JIS/VOL20/Toth/toth25.html">Alternating Sums Concerning Multiplicative Arithmetic Functions</a>, Journal of Integer Sequences, Vol. 20 (2017), Article 17.2.1.
%F A370896 a(n) = Sum_{k=1..n} (-1)^(k+1) * A007947(k).
%F A370896 a(n) = c * n^2 + O(R(n)), where c = A065463 / 10 = 0.07044422..., R(n) = x^(3/2)*exp(-c_1*log(n)^(3/5)/log(log(n))^(1/5)) unconditionally, or x^(7/5)*exp(c_2*log(n)/log(log(n))) assuming the Riemann hypothesis, and c_1 and c_2 are positive constants (Tóth, 2017).
%t A370896 rad[n_] := Times @@ (First[#]& /@ FactorInteger[n]); Accumulate[Array[(-1)^(#+1) * rad[#] &, 100]]
%o A370896 (PARI) rad(n) = vecprod(factor(n)[, 1]);
%o A370896 lista(kmax) = {my(s = 0); for(k = 1, kmax, s += (-1)^(k+1) * rad(k); print1(s, ", "))};
%Y A370896 Cf. A007947, A065463, A073355.
%Y A370896 Similar sequences: A068762, A068773, A307704, A357817, A362028.
%K A370896 sign,easy
%O A370896 1,3
%A A370896 _Amiram Eldar_, Mar 05 2024