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

1,3

Comments

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

Links

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

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).

Example

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,
  ...

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A277760 A371572 A127704 * A050873 A324668 A128221

Adjacent sequences: A307659 A307660 A307661 * A307663 A307664 A307665

Keyword

nonn,tabl

Author

I. V. Serov, Apr 20 2019

Status

approved