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%I #22 Aug 14 2020 15:01:09
%S 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,
%T 55,40,65,30,109,32,63,53,71,51,107,38,79,62,99,42,145,44,95,83,95,48,
%U 143,57,123,80,111,54,161,74,129,89,119,60,223,62,127,109,127,87,217
%N a(n) = n-th positive integer relatively prime to n.
%C Smallest k such there are exactly n integers among (1,2,3,4,...,k) relatively prime to n. - _Benoit Cloitre_, Jun 09 2002
%H Reinhard Zumkeller, <a href="/A069213/b069213.txt">Table of n, a(n) for n = 1..10000</a>
%F 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
%F 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
%e 6 is relatively prime to 1, 5, 7, 11, 13, 17,..., the 6th term of this sequence being 17, so a(6) = 17.
%t 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 *)
%t Table[Position[CoprimeQ[Range[300],n],True,1,n][[-1]],{n,70}]//Flatten (* _Harvey P. Dale_, Aug 14 2020 *)
%o (PARI) for(n=1,100,s=1; while(sum(i=1,s,if(gcd(n,i)-1,0,1))<n,s++); print1(s,","))
%o (Haskell)
%o a069213 = last . a077581_row -- _Reinhard Zumkeller_, Sep 26 2014
%Y Final term of n-th row of A077581.
%Y Cf. A077582.
%Y Cf. A247798, A247815.
%K nonn
%O 1,2
%A _Leroy Quet_, Apr 11 2002
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