A069213 a(n) = n-th positive integer relatively prime to n.

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

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))<n, s++); print1(s, ", "))
(Haskell)
a069213 = last . a077581_row  -- Reinhard Zumkeller, Sep 26 2014

Crossrefs

Final term of n-th row of A077581.

Cf. A077582.

Cf. A247798, A247815.

Sequence in context: A346193 A244974 A077580 * A130700 A117134 A334127

Adjacent sequences: A069210 A069211 A069212 * A069214 A069215 A069216

Keyword

nonn

Author

Leroy Quet, Apr 11 2002

Status

approved