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 A091555 #18 Nov 30 2024 11:03:21
%S A091555 1,1,0,-1,-3,-4,-6,-8,-10,-11,-13,-15,-18,-20,-21,-22,-24,-26,-29,-32,
%T A091555 -34,-35,-37,-39,-41,-42,-43,-44,-46,-49,-53,-57,-60,-62,-63,-64,-66,
%U A091555 -67,-67,-67,-68,-70,-73,-76,-79,-81,-84,-87,-90,-93,-95,-97,-100,-103,-105,-107
%N A091555 Partial sums of Mertens's function (A002321).
%H A091555 Indranil Ghosh, <a href="/A091555/b091555.txt">Table of n, a(n) for n = 1..5000</a>
%F A091555 a(n) = Sum_{k=1..n} mu(k)*(n-k+1) where mu=A008683, the Moebius function. - _Reinhard Zumkeller_, Nov 06 2006
%F A091555 G.f.: (1/(1 - x)^2)*Sum_{k>=1} mu(k)*x^k. - _Ilya Gutkovskiy_, Mar 11 2018
%t A091555 Table[Sum[MoebiusMu[k] (n - k + 1), {k, 1, n}], {n , 1, 56}] (* _Indranil Ghosh_, Mar 16 2017 *)
%t A091555 Accumulate[Table[Sum[MoebiusMu[k], {k, 1, n}], {n, 1, 100}]] (* _Vaclav Kotesovec_, Nov 30 2024 *)
%o A091555 (PARI) for(n=1, 56, print1(sum(k=1, n, moebius(k) * (n - k + 1)),", ")) \\ _Indranil Ghosh_, Mar 16 2017
%Y A091555 Cf. A002321, A008683.
%K A091555 sign
%O A091555 1,5
%A A091555 _Jon Perry_, Mar 04 2004
%E A091555 More terms from _Reinhard Zumkeller_, Nov 06 2006