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 A359188 #17 Aug 27 2023 17:03:21 %S A359188 1,1,2,0,4,-11,6,-24,-18,-79,10,-276,12,-447,-464,-1008,16,-3636,18, %T A359188 -5580,-5228,-11263,22,-41184,-3100,-53247,-59022,-116004,28,-454501, %U A359188 30,-524256,-649868,-1114111,-121344,-4438368,36,-4980735,-6909200,-11106720,40,-44114197,42 %N A359188 a(n) = Sum_{d|n} mu(n/d) * d * (n/d)^(d-1), where mu() is the Moebius function (A008683). %F A359188 G.f.: Sum_{k>=1} mu(k) * x^k/(1 - k * x^k)^2. %F A359188 If p is prime, a(p) = p - 1. %t A359188 a[n_] := DivisorSum[n, MoebiusMu[n/#] * # * (n/#)^(#-1) &]; Array[a, 45] (* _Amiram Eldar_, Aug 27 2023 *) %o A359188 (PARI) a(n) = sumdiv(n, d, moebius(n/d)*d*(n/d)^(d-1)); %o A359188 (PARI) my(N=50, x='x+O('x^N)); Vec(sum(k=1, N, moebius(k)*x^k/(1-k*x^k)^2)) %Y A359188 Cf. A000010, A008683, A167531, A359103. %K A359188 sign %O A359188 1,3 %A A359188 _Seiichi Manyama_, Dec 19 2022