A062778 Values of Moebius-transform of PrimePi function.

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

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: A081171 A334594 A359336 * A363620 A363624 A108202

Adjacent sequences: A062775 A062776 A062777 * A062779 A062780 A062781

Keyword

nonn

Author

Labos Elemer, Jul 18 2001

Status

approved