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A307662
Triangle T(i,j=1..i) read by rows which contain the naturally ordered divisors-or-ones of the row number i.
2
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
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
KEYWORD
nonn,tabl
AUTHOR
I. V. Serov, Apr 20 2019
STATUS
approved