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A181834
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The number of primes <= n that are strongly prime to n.
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10
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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
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0,9
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COMMENTS
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k is strongly prime to n iff k is relatively prime to n and k does not divide n-1.
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LINKS
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EXAMPLE
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a(11) = card(primes in {3, 4, 6, 7, 8, 9}) = card({3, 7}) = 2.
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MAPLE
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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)):
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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