A048863 Number of nonprimes (1 and composites) in the reduced residue system of n-th primorial number (A002110).

1, 1, 1, 1, 6, 142, 2518, 49836, 1012859, 24211838, 721500294, 22627459401, 844130935668, 34729870646918, 1491483322755274, 69890000837179157, 3692723747920861125, 217158823263305180123, 13182405032836651359192, 879055475442725460400606

Offset: 0

Author

Labos Elemer

Keywords

• nonn
• more

Examples

			For n = 3, the 3rd primorial is 30, phi(30) = 8, a(3) = 1 since 1 is nonprime. See A048597.
For n = 4, the 4th primorial is 210, the size of its reduced residue system (RRS) is 48 of which 6 are either composite numbers or 1: {1, 121, 143, 169, 187, 209}.
		

Links

• Kim Walisch, Fast C++ prime counting function implementation (primecount).

Crossrefs

Cf. A000010 (phi), A000720, A002110, A005867, A007625, A048597, A048862.

Programs

Mathematica

Table[Function[P, EulerPhi@ P - # &[PrimePi@ P - n]]@ Product[Prime@ i, {i, n}], {n, 0, 12}] (* Michael De Vlieger, May 08 2017 *)

Formula

a(n) = A005867(n) - A000849(n) + n.

a(n) = A000010(A002110(n)) - A000720(A002110(n)) + A001221(A002110(n)).

Extensions

a(14)-a(15) from Max Alekseyev, Aug 21 2013

a(0) prepended, a(15) corrected, a(16)-a(17) computed from A000849 by Max Alekseyev, Feb 21 2016

a(18)-a(19) calculated using Kim Walisch's primecount and added by Amiram Eldar, Sep 03 2024