cp's OEIS Frontend

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.

A087989 a(n) = M(n!), the value of Mertens's function at the n-th factorial.

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%I A087989 #29 Nov 10 2024 09:24:13
%S A087989 1,1,0,-1,-2,-3,-3,-6,-15,-138,-26,-527,-3474,-19550,-20014,3084,
%T A087989 -1253696,7121000,-18636176,-44667415,94933922,-848322099
%N A087989 a(n) = M(n!), the value of Mertens's function at the n-th factorial.
%H A087989 Marc Deléglise and Joël Rivat, <a href="http://projecteuclid.org/euclid.em/1047565447">Computing the summation of the Mobius function</a>, Experiment. Math. 5:4 (1996), pp. 291-295.
%F A087989 a(n) = A002321(A000142(n)).
%e A087989 a(4) = A002321(4!) = A002321(24) = -2.
%t A087989 s=0; i=1; Do[While[i<= n!, s=s+MoebiusMu[i]; i++ ]; Print[s], {n, 0, 10}]
%o A087989 (PARI) a(n)=sum(k=1,n!,moebius(k)) \\ _Charles R Greathouse IV_, Apr 02 2014
%Y A087989 Cf. A000142, A002321, A084237, A087987.
%K A087989 more,sign
%O A087989 0,5
%A A087989 _Labos Elemer_, Oct 02 2003
%E A087989 More terms from _Sean A. Irvine_, Dec 06 2009
%E A087989 a(14) from _Donovan Johnson_, Jun 21 2012
%E A087989 a(15)-a(17) from _Rikard Nordgren_, Nov 10 2012
%E A087989 a(18)-a(21) from _Henri Lifchitz_, Nov 10 2024