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

Offset

1,3

Links

Table of n, a(n) for n=1..14.

Marc Deléglise and Joël Rivat, Computing the summation of the Mobius function, Experiment. Math. 5:4 (1996), pp. 291-295.

Formula

a(n) = A002321(A002110(n)).

Example

n = 3: 3rd primorial number = 30. A002321(30) = -3.

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

Prog

(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
(Perl) use ntheory ":all"; say mertens(pn_primorial($_)) for 1..12; # Dana Jacobsen, May 22 2015

Crossrefs

Cf. A002110, A002321, A008683, A084237.

Sequence in context: A156690 A228900 A060325 * A290311 A322790 A333560

Adjacent sequences: A087984 A087985 A087986 * A087988 A087989 A087990

Keyword

more,sign

Author

Labos Elemer, Oct 02 2003

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

Status

approved