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Difference between number of nonprimes and primes in reduced residue system of primorial numbers.
0

%I #11 May 09 2017 08:04:11

%S 1,1,0,-6,-36,-196,-724,7512,366838,11928316,421130508,14598816402,

%T 584642184936,25314953837836,1128885572358548,54492272309366314,

%U 2950485568862138250,213151926413154110951

%N Difference between number of nonprimes and primes in reduced residue system of primorial numbers.

%F a(n) = A048863(n) - A048862(n) = A048866(A002110(n)).

%F a(n) = A005867(n) - 2*A000849(n) + 2*n.

%e n=4, Q(4)=2*3*5*7=210, reduced residue system includes 48 terms:42 primes and 6 composites and 1: a(4)=6-42=-36.

%t Table[Function[P, EulerPhi@ P - 2 # &[PrimePi@ P - n]]@ Product[Prime@ i, {i, n}], {n, 0, 12}] (* _Michael De Vlieger_, May 08 2017 *)

%Y Cf. A048868, A048867, A048597, A002110, A048862, A048863, A048866.

%K sign

%O 0,4

%A _Labos Elemer_

%E Corrected and extended by _Max Alekseyev_, Feb 22 2016