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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
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
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.
Sequence in context: A346193 A244974 A077580 * A130700 A117134 A334127
KEYWORD
nonn
AUTHOR
Leroy Quet, Apr 11 2002
STATUS
approved