A307662 Triangle T(i,j=1..i) read by rows which contain the naturally ordered divisors-or-ones of the row number i.

1, 1, 2, 1, 1, 3, 1, 2, 1, 4, 1, 1, 1, 1, 5, 1, 2, 3, 1, 1, 6, 1, 1, 1, 1, 1, 1, 7, 1, 2, 1, 4, 1, 1, 1, 8, 1, 1, 3, 1, 1, 1, 1, 1, 9, 1, 2, 1, 1, 5, 1, 1, 1, 1, 10, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 11, 1, 2, 3, 4, 1, 6, 1, 1, 1, 1, 1, 12, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 13

Offset: 1

Author

I. V. Serov, Apr 20 2019

Keywords

• nonn
• tabl

Comments

Replace 0 with 1 in A127093. - Omar E. Pol, Apr 21 2019

Examples

			Triangle begins:
  1,
  1, 2,
  1, 1, 3,
  1, 2, 1, 4,
  1, 1, 1, 1, 5,
  1, 2, 3, 1, 1, 6,
  1, 1, 1, 1, 1, 1, 7,
  1, 2, 1, 4, 1, 1, 1, 8,
  1, 1, 3, 1, 1, 1, 1, 1, 9,
  1, 2, 1, 1, 5, 1, 1, 1, 1,10,
  1, 1, 1, 1, 1, 1, 1, 1, 1, 1,11,
  1, 2, 3, 4, 1, 6, 1, 1, 1, 1, 1,12,
  ...
		

Links

• I. V. Serov, Rows n = 1..131 of triangle, flattened

Crossrefs

Cf. A100995, A127093, A307641, A027750, A002024, A002260.

Programs

Mathematica

Table[Map[If[Mod[n, #] == 0, #, 1] &, Range@ n], {n, 13}] // Flatten (* Michael De Vlieger, Apr 23 2019 *)

PARI

row(n) = vector(n, k, if ((n % k) == 0, k, 1)); \\ Michel Marcus, Apr 21 2019

Formula

For j=1..floor(i/2), T(i,j)=T(i-j,j).

For j=floor(i/2)+1..i-1, T(i,j)=1.

T(i,i) = i.

Let i = A002024(n) and j = A002260(n):

a(n) = a((i-j-1)*(i-j)/2+j) if j=1..floor(i/2).

a(n) = 1 if j=floor(i/2)+1..i-1.

a(n) = i if j=i.

T(i,j) = a(n).