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A062778 Values of Moebius-transform of PrimePi function. 1
0, 1, 2, 1, 3, 0, 4, 2, 2, 0, 5, 1, 6, 1, 1, 2, 7, 2, 8, 3, 2, 2, 9, 2, 6, 2, 5, 2, 10, 3, 11, 5, 4, 3, 4, 2, 12, 3, 4, 2, 13, 3, 14, 5, 6, 4, 15, 4, 11, 5, 6, 5, 16, 4, 8, 5, 6, 5, 17, 2, 18, 6, 8, 7, 9, 4, 19, 7, 8, 6, 20, 5, 21, 8, 9, 8, 12, 6, 22, 8, 13, 8, 23, 6, 13, 8, 11, 7, 24, 4, 14, 9, 11, 8 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Harry J. Smith, Table of n, a(n) for n = 1..1000

FORMULA

a(n) = Sum_{d|n} pi(n/d)*mu(d).

EXAMPLE

n=12, divisors = D(12) = {1,2,3,4,6,12}, pi(12/divisors) = {5,3,2,2,1,0}, mu(divisors) = {1,-1,-1,0,1,0}, Sum = 5*1 - 3*1 - 2*1 + 0 + 1*1 + 0 = 1, thus a(12)=1; for p=prime(n), pi(p/divisor) = {n,0}, mu({1,p})={1,-1}, Sum = 1*n + 0 = n, so a(prime(n)) = n.

MATHEMATICA

f[n_] := Block[{d = Divisors@n}, Plus @@ (MoebiusMu /@ (n/d)*PrimePi /@ d)]; Array[f, 94] (* Robert G. Wilson v, Dec 07 2005 *)

PROG

(PARI) { for (n=1, 1000, d=divisors(n); write("b062778.txt", n, " ", sum(k=1, length(d), primepi(n/d[k]) * moebius(d[k]))) ) } \\ Harry J. Smith, Aug 10 2009

(PARI) a(n) = sumdiv(n, d, primepi(d)*moebius(n/d)); \\ Michel Marcus, Nov 05 2018

CROSSREFS

Cf. A007444, A007445.

Sequence in context: A278529 A160588 A081171 * A108202 A025480 A088002

Adjacent sequences:  A062775 A062776 A062777 * A062779 A062780 A062781

KEYWORD

nonn

AUTHOR

Labos Elemer, Jul 18 2001

STATUS

approved

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Last modified February 28 23:19 EST 2020. Contains 332353 sequences. (Running on oeis4.)