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).

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

1,3

Links

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

Example

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)

Maple

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);

Mathematica

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 *)

Prog

(PARI)
A129321row_n(n) ={my(r = vector(n), x=1, i=1 ); while(i<n+1, if(gcd(x, n*(n+1)/2)==1, r[i] = x; i+=1, ); x+=1); r} \\ John Tyler Rascoe, Mar 20 2024

Crossrefs

Cf. A124823.

Sequence in context: A349015 A217105 A143892 * A064642 A193630 A144505

Adjacent sequences: A129318 A129319 A129320 * A129322 A129323 A129324

Keyword

nonn,tabl

Author

Leroy Quet, May 26 2007

Status

approved