A057859 - OEIS

%I #14 May 13 2017 21:05:07

%S 1,2,3,3,5,4,7,5,7,6,11,6,13,8,10,9,17,8,19,10,14,12,23,10,21,14,19,

%T 14,29,11,31,17,22,18,26,14,37,20,26,18,41,15,43,22,26,24,47,18,43,22,

%U 34,26,53,20,42,26,38,30,59,19,61,32,38,33,50,23,67,34,46

%N Number of residue classes modulo n which contain a prime.

%C a(n) = n iff n is prime; a(2*n)<=n+1; a(4*p)=2*p for primes p>2: a(A001749(n))=A057860(A001749(n)). - _Reinhard Zumkeller_, Jan 11 2004

%H Alois P. Heinz, <a href="/A057859/b057859.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A000010(n) + A001221(n) = n - A057860(n).

%e a(30) = 11 since 30k+m can be prime if m = 2, 3 or 5 (once each with k = 0) or m = 1, 7, 11, 13, 17, 19, 23 or 29 (each for an infinite number of values of k).

%p with(numtheory):

%p a:= n-> phi(n)+nops(factorset(n)):

%p seq(a(n), n=1..100);  # _Alois P. Heinz_, Jul 14 2016

%t Table[EulerPhi[n] + PrimeNu[n], {n, 1, 100}] (* _G. C. Greubel_, May 13 2017 *)

%o (PARI) for(n=1,100, print1(eulerphi(n) + omega(n), ", ")) \\ _G. C. Greubel_, May 13 2017

%Y Cf. A057857, A179179.

%K nonn,look

%O 1,2

%A _Henry Bottomley_, Sep 08 2000