

A088004


"Truncated Mertens function": values of 1 at primes are left out, that is, summatory Moebius when argument runs through nonprimes.


6



1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 5, 5, 5, 5, 5, 5, 6, 7, 7, 7, 7, 8, 8, 8, 8, 7, 7, 7, 8, 9, 10, 10, 10, 11, 12, 12, 12, 11, 11, 11, 11, 12, 12, 12, 12, 12, 13, 13, 13, 13, 14, 14, 15, 16, 16, 16, 16, 17, 17, 17, 18, 17, 17, 17, 18, 17, 17, 17, 17, 18, 18, 18, 19, 18, 18, 18, 18
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,6


COMMENTS

Since the principal source of negative excursions of the Mertens function is here eliminated, most probably this sequence increases ad infinitum albeit nonmonotonically; it decreases at squarefree numbers with an odd number of prime divisors, e.g., 30 and 42.
Positions of records of a(n) are in A030229.  Michael De Vlieger, May 15 2017


LINKS

Michael De Vlieger, Table of n, a(n) for n = 1..10000


FORMULA

a(n) = A002321(n)  (1)*pi(n) = A002321(n) + A000720(n).


MATHEMATICA

mer[x_] := mer[x1]+MoebiusMu[x]; mer[0]=0; $RecursionLimit=1000; Table[mer[w]+PrimePi[w], {w, 1, 256}]
(* Second program: *)
Accumulate@ Array[MoebiusMu@ # + Boole[PrimeQ@ #] &, 81] (* Michael De Vlieger, May 15 2017 *)


CROSSREFS

Cf. A000720, A002321, A008683, A030229.
Sequence in context: A029269 A272187 A194621 * A070548 A209628 A132011
Adjacent sequences: A088001 A088002 A088003 * A088005 A088006 A088007


KEYWORD

nonn


AUTHOR

Labos Elemer, Oct 14 2003


STATUS

approved



