A247815 -id:A247815 - cp's OEIS frontend

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

Leroy Quet, Apr 11 2002

nonn

Smallest k such there are exactly n integers among (1,2,3,4,...,k) relatively prime to n. - Benoit Cloitre, Jun 09 2002

			6 is relatively prime to 1, 5, 7, 11, 13, 17,..., the 6th term of this sequence being 17, so a(6) = 17.

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Final term of n-th row of A077581.
Cf. A077582.
Cf. A247798, A247815.

a069213 = last . a077581_row  -- Reinhard Zumkeller, Sep 26 2014

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 *)

for(n=1,100,s=1; while(sum(i=1,s,if(gcd(n,i)-1,0,1))

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

A077581 Triangle in which row n contains the n smallest numbers starting from 1 and coprime to n.

Original entry on oeis.org

1, 1, 3, 1, 2, 4, 1, 3, 5, 7, 1, 2, 3, 4, 6, 1, 5, 7, 11, 13, 17, 1, 2, 3, 4, 5, 6, 8, 1, 3, 5, 7, 9, 11, 13, 15, 1, 2, 4, 5, 7, 8, 10, 11, 13, 1, 3, 7, 9, 11, 13, 17, 19, 21, 23, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 1, 5, 7, 11, 13, 17, 19, 23, 25, 29, 31, 35, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12

Offset: 1

Amarnath Murthy, Nov 14 2002

A247815 and A247892 give number of primes and nonprimes per row. - Reinhard Zumkeller, Sep 26 2014

			1;
1,  3;
1,  2,  4;
1,  3,  5,  7;
1,  2,  3,  4,  6;
1,  5,  7, 11, 13, 17;
1,  2,  3,  4,  5,  6,  8;
1,  3,  5,  7,  9, ...

Reinhard Zumkeller, Rows n = 1..125 of triangle, flattened

Cf. A069213, A077582.
Cf. A247798 (central terms), A247815, A247892.
Cf. A077664.

a077581 n k = a077581_tabl !! (n-1) !! (k-1)
a077581_row n = a077581_tabl !! (n-1)
a077581_tabl = map (\x -> take x [z | z <- [1..], gcd x z == 1]) [1..]
-- Reinhard Zumkeller, Sep 26 2014

row[n_] := Take[Select[Range[n^2], GCD[ #, n]==1&], n]; Join@@row/@Range[13]

More terms from Sascha Kurz, Jan 11 2003

A247892 Number of nonprimes in n-th row of triangle A077581.

Original entry on oeis.org

1, 1, 2, 1, 3, 1, 4, 3, 4, 3, 7, 3, 8, 5, 8, 6, 11, 4, 12, 7, 11, 9, 15, 6, 15, 12, 16, 12, 20, 4, 21, 15, 19, 16, 22, 10, 26, 18, 23, 17, 29, 11, 30, 22, 24, 24, 33, 16, 34, 22, 31, 25, 38, 19, 36, 27, 35, 30, 43, 15, 44, 33, 36, 34, 44, 22, 49, 36, 43, 27

Offset: 1

Reinhard Zumkeller, Sep 26 2014

nonn

a(n) = n - A247815(n)

Cf. A077581, A247815.

Haskell
```
a247892 n = n - a247815 n
```

cp's OEIS Frontend

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

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A077581 Triangle in which row n contains the n smallest numbers starting from 1 and coprime to n.

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A247892 Number of nonprimes in n-th row of triangle A077581.

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Haskell