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A086685
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Number of 1 <= i < n such that i*n+1 is prime.
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1
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0, 1, 1, 2, 1, 4, 2, 2, 3, 5, 3, 6, 4, 5, 5, 5, 3, 10, 2, 6, 6, 9, 4, 9, 5, 9, 7, 11, 4, 17, 3, 10, 9, 12, 9, 15, 4, 9, 11, 13, 5, 21, 7, 11, 10, 16, 8, 19, 6, 18, 13, 17, 5, 23, 10, 18, 9, 16, 8, 27, 7, 15, 13, 16, 13, 29, 9, 18, 13, 27, 9, 26, 10, 19, 18, 17, 11, 29, 11, 23, 18, 22, 11, 32
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OFFSET
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1,4
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COMMENTS
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Number of primes p < n^2 such that p == 1 (mod n). The standard conjecture here is that a(n) ~ n^2/(2 phi(n)log n), where Euler's totient function phi(n) = A000010(n). - Thomas Ordowski, Oct 21 2014
Number of primes appearing in the 1st column of an n X n square array whose elements are the numbers from 1..n^2, listed in increasing order by rows. - Wesley Ivan Hurt, May 17 2021
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LINKS
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FORMULA
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a(n) = Sum_{k=1..n} pi(1+n*(k-1)) - pi(n*(k-1)), where pi is the prime counting function. - Wesley Ivan Hurt, May 17 2021
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EXAMPLE
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For n=10, i=1,3,4,6,7 give primes, so a(10)=5.
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MATHEMATICA
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f[n_] := Length[ Select[ Range[n - 1], PrimeQ[n# + 1] & ]]; Table[ f[n], {n, 1, 85}]
Table[Count[Range[n-1]n+1, _?PrimeQ], {n, 90}] (* Harvey P. Dale, Oct 10 2013 *)
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PROG
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(PARI) nphi(n)=local(c); c=0; for (i=1, n-1, if (isprime(i*n+1), c++)); c for(i=1, 60, print1(", "nphi(i)))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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