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A057859 Number of residue classes modulo n which contain a prime. 4
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, 14, 29, 11, 31, 17, 22, 18, 26, 14, 37, 20, 26, 18, 41, 15, 43, 22, 26, 24, 47, 18, 43, 22, 34, 26, 53, 20, 42, 26, 38, 30, 59, 19, 61, 32, 38, 33, 50, 23, 67, 34, 46 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..10000

FORMULA

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

EXAMPLE

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).

MAPLE

with(numtheory):

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

seq(a(n), n=1..100);  # Alois P. Heinz, Jul 14 2016

MATHEMATICA

Table[EulerPhi[n] + PrimeNu[n], {n, 1, 100}] (* G. C. Greubel, May 13 2017 *)

PROG

(PARI) for(n=1, 100, print1(eulerphi(n) + omega(n), ", ")) \\ G. C. Greubel, May 13 2017

CROSSREFS

Cf. A057857, A179179.

Sequence in context: A064920 A064916 A062854 * A242992 A029579 A106647

Adjacent sequences:  A057856 A057857 A057858 * A057860 A057861 A057862

KEYWORD

nonn,look

AUTHOR

Henry Bottomley, Sep 08 2000

STATUS

approved

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Last modified October 15 12:02 EDT 2018. Contains 316232 sequences. (Running on oeis4.)