A124823 -id:A124823 - cp's OEIS frontend

A124822 a(n) = the n-th integer from among those positive integers which are coprime to n(n+1).

1, 5, 7, 9, 17, 19, 15, 23, 31, 27, 35, 37, 31, 59, 53, 33, 53, 55, 49, 83, 79, 49, 71, 89, 67, 83, 95, 67, 109, 113, 63, 103, 113, 103, 151, 109, 79, 127, 157, 101, 145, 149, 95, 179, 173, 97, 143, 167, 141, 197, 175, 113, 161, 223, 173, 199, 185, 121, 223, 227, 127, 223

Offset: 1

Leroy Quet, Nov 08 2006

nonn

			The positive integers which are coprime to (5*6) are 1,7,11,13,17,19,23,29,... The fifth of these integers is 17, so a(5) = 17.

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A124823.

f[n_] := Block[{k = 0, c = n},While[c > 0,k++;While[GCD[n*(n + 1), k] > 1, k++ ];c--;];k];Table[f[n], {n, 65}] (* Ray Chandler, Nov 10 2006 *)
Table[Select[Range[n(n+1)],CoprimeQ[#,n(n+1)]&][[n]],{n,70}] (* Harvey P. Dale, May 01 2016 *)

Extended by Ray Chandler, Nov 10 2006

A129321 Triangle where the n-th row is the smallest n positive integers which are coprime to the n-th triangular number (n(n+1)/2).

Original entry on oeis.org

1, 1, 2, 1, 5, 7, 1, 3, 7, 9, 1, 2, 4, 7, 8, 1, 2, 4, 5, 8, 10, 1, 3, 5, 9, 11, 13, 15, 1, 5, 7, 11, 13, 17, 19, 23, 1, 2, 4, 7, 8, 11, 13, 14, 16, 1, 2, 3, 4, 6, 7, 8, 9, 12, 13, 1, 5, 7, 13, 17, 19, 23, 25, 29, 31, 35, 1, 5, 7, 11, 17, 19, 23, 25, 29, 31, 35, 37, 1, 2, 3, 4, 5, 6, 8, 9, 10, 11

Offset: 1

Leroy Quet, May 26 2007

			The 6th triangular number is 21. So row 6 gives the six smallest positive integers which are coprime to 21: (1,2,4,5,8,10).
From _John Tyler Rascoe_, Mar 20 2024: (Start)
Triangle begins:
  1;
  1, 2;
  1, 5, 7;
  1, 3, 7, 9;
  1, 2, 4, 7, 8;
  1, 2, 4, 5, 8, 10;
(End)

John Tyler Rascoe, Rows n = 1..141, flattened

Cf. A124823.

A129321 := proc(nrow) local a,n; a := [] ; n := 1; while nops(a) < nrow do if gcd(n, nrow*(nrow+1)/2) = 1 then a := [op(a),n] ; fi ; n := n+1 ; od: RETURN(a) ; end: seq( op(A129321(n)),n=1..15);

A129321row[n_] := Block[{t = n*(n+1)/2, c = 0}, Table[While[!CoprimeQ[++c, t]]; c, n]]; Array[A129321row, 10] (* Paolo Xausa, Mar 20 2024 *)

A129321row_n(n) ={my(r = vector(n), x=1, i=1 ); while(iJohn Tyler Rascoe, Mar 20 2024

cp's OEIS Frontend

A124822 a(n) = the n-th integer from among those positive integers which are coprime to n(n+1).

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