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A069213
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a(n) = n-th positive integer relatively prime to n.
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14
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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; internal format)
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OFFSET
| 1,2
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COMMENTS
| Smallest k such there are exactly n integers among (1,2,3,4,...,k) relatively prime to n. - Benoit Cloitre (benoit7848c(AT)orange.fr), Jun 09 2002
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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 (amarnath_murthy(AT)yahoo.com), 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 (amarnath_murthy(AT)yahoo.com), Jul 07 2002
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EXAMPLE
| 6 is relatively prime to 1, 5, 7, 11, 13, 17,..., the 6_th term of this sequence being 17, so a(6) = 17.
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MATHEMATICA
| f[n_] := Block[{c = 0, k = 1}, While[c < n, If[CoprimeQ[k, n], c++ ]; k++ ]; k - 1]; Array[f, 66] [From Robert G. Wilson v (rgwv(AT)rgwv.com), Sep 10 2008]
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PROG
| (PARI) for(n=1, 100, s=1; while(sum(i=1, s, if(gcd(n, i)-1, 0, 1))<n, s++); print1(s, ", "))
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CROSSREFS
| Final term of n-th row of A077581.
Cf. A077582.
Sequence in context: A003981 A053480 A077580 * A130700 A117134 A095001
Adjacent sequences: A069210 A069211 A069212 * A069214 A069215 A069216
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KEYWORD
| nonn
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AUTHOR
| Leroy Quet Apr 11 2002
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