A087987 a(n) is the Mertens function value at the n-th primorial number.
0, -1, -3, -1, -1, 16, -25, 278, 3516, -5012, -30431, -234676, -4247453, -6271957, 177533446, -416214476
Offset: 1
Examples
n = 3: 3rd primorial number = 30. A002321(30) = -3.
Links
- Marc Deléglise and Joël Rivat, Computing the summation of the Mobius function, Experiment. Math. 5:4 (1996), pp. 291-295.
Programs
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Mathematica
q[x_] := Apply[Times, Table[Prime[i], {i, 1, x}]] s=0; i=1; Do[While[i<=q[n], s=s+MoebiusMu[i]; i++ ]; Print[s], {n, 0, 8}]//Timing -
PARI
p=1; s=1; for(n=1,10,pr=p; p*=prime(n); s+=sum(k=pr+1, p, moebius(k)); print1(s",")) \\ Herman Jamke (hermanjamke(AT)fastmail.fm), Dec 21 2007
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Perl
use ntheory ":all"; say mertens(pn_primorial($)) for 1..12; # _Dana Jacobsen, May 22 2015
Extensions
One more term from Herman Jamke (hermanjamke(AT)fastmail.fm), Dec 21 2007
a(10)-a(11) from Donovan Johnson, Jun 21 2012
a(12)-a(13) from Rikard Nordgren, Nov 11 2012
a(14) from Chai Wah Wu, Apr 24 2021
a(15)-a(16) from Henri Lifchitz, Nov 10 2024