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 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 non-monotonically; 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[x-1]+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

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Last modified October 16 16:18 EDT 2019. Contains 328101 sequences. (Running on oeis4.)