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

Offset

0,5

Links

Table of n, a(n) for n=0..17.

Formula

a(n) = A005867(n) - A000849(n) + n = A000010(A002110(n)) - A000720(A002110(n)) + A001221(A002110(n)).

Example

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

Mathematica

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

Crossrefs

Cf. A002110, A000010, A005867, A000720, A048597, A007625, A048862.

Sequence in context: A225810 A067196 A286446 * A363989 A278356 A277419

Adjacent sequences: A048860 A048861 A048862 * A048864 A048865 A048866

Keyword

nonn,more

Author

Labos Elemer

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

Status

approved