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 A069213 a(n) = n-th positive integer relatively prime to n. 17
 1, 3, 4, 7, 6, 17, 8, 15, 13, 23, 12, 35, 14, 31, 28, 31, 18, 53, 20, 49, 37, 47, 24, 71, 31, 55, 40, 65, 30, 109, 32, 63, 53, 71, 51, 107, 38, 79, 62, 99, 42, 145, 44, 95, 83, 95, 48, 143, 57, 123, 80, 111, 54, 161, 74, 129, 89, 119, 60, 223, 62, 127, 109, 127, 87, 217 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Smallest k such there are exactly n integers among (1,2,3,4,...,k) relatively prime to n. - Benoit Cloitre, Jun 09 2002 LINKS Reinhard Zumkeller, Table of n, a(n) for n = 1..10000 FORMULA a(p) = p+1, p is a prime, a(2^n)= 2^(n+1) - 1. What are a(pq), a(pqr), a(n) where n the product of first k primes? - Amarnath Murthy, Nov 14 2002 Let the remainder when n is divided by phi(n) be r and the quotient be k. I.e., n = k*phi(n) + r. Then k*n + r < a(n) < (k+1)*n. If the phi(n) numbers be arranged in increasing order and if the r-th number is m then a(n) = k*n + m. - Amarnath Murthy, Jul 07 2002 EXAMPLE 6 is relatively prime to 1, 5, 7, 11, 13, 17,..., the 6th term of this sequence being 17, so a(6) = 17. MATHEMATICA f[n_] := Block[{c = 0, k = 1}, While[c < n, If[CoprimeQ[k, n], c++ ]; k++ ]; k - 1]; Array[f, 66] (* Robert G. Wilson v, Sep 10 2008 *) Table[Position[CoprimeQ[Range[300], n], True, 1, n][[-1]], {n, 70}]//Flatten (* Harvey P. Dale, Aug 14 2020 *) PROG (PARI) for(n=1, 100, s=1; while(sum(i=1, s, if(gcd(n, i)-1, 0, 1))

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Last modified January 18 17:18 EST 2022. Contains 350455 sequences. (Running on oeis4.)