A181834 - OEIS

A181834

The number of primes <= n that are strongly prime to n.

0, 0, 0, 0, 0, 1, 0, 1, 2, 2, 1, 2, 2, 3, 3, 2, 3, 5, 4, 5, 5, 4, 4, 6, 6, 6, 6, 6, 6, 7, 6, 7, 9, 8, 7, 7, 7, 9, 9, 8, 8, 10, 9, 10, 11, 10, 10, 12, 12, 12, 12, 11, 11, 13, 13, 12, 12, 12, 12, 14, 13, 14, 15, 14, 15, 15, 13, 15, 16, 15, 14, 16, 17

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OFFSET

0,9

COMMENTS

k is strongly prime to n iff k is relatively prime to n and k does not divide n-1.

LINKS

Table of n, a(n) for n=0..72.

Peter Luschny, Strong coprimality.

EXAMPLE

a(11) = card(primes in {3, 4, 6, 7, 8, 9}) = card({3, 7}) = 2.

MAPLE

with(numtheory):

Primes := n -> select(k->isprime(k), {$1..n}):

StrongCoprimes := n -> select(k->igcd(k, n)=1, {$1..n}) minus divisors(n-1):

StrongCoprimePrimes := n -> Primes(n) intersect StrongCoprimes(n):

A181834 := n -> nops(StrongCoprimePrimes(n)):

MATHEMATICA

strongCoprimeQ[k_, n_] := PrimeQ[k] && CoprimeQ[n, k] && !Divisible[n-1, k]; a[n_] := Select[Range[n], strongCoprimeQ[#, n]&] // Length; Table[a[n], {n, 0, 72}] (* Jean-François Alcover, Jul 23 2013 *)

CROSSREFS

Cf. A181830, A181831, A181832, A181833, A181835, A181836, A048865.

Sequence in context: A245588 A014420 A029289 * A194848 A289497 A029328

Adjacent sequences: A181831 A181832 A181833 * A181835 A181836 A181837

KEYWORD

nonn

AUTHOR

Peter Luschny, Nov 17 2010

STATUS

approved