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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
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
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
KEYWORD
nonn
AUTHOR
Labos Elemer, Oct 14 2003
STATUS
approved