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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.

%I A307662 #75 May 01 2019 10:26:13
%S A307662 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,
%T A307662 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,
%U A307662 2,3,4,1,6,1,1,1,1,1,12,1,1,1,1,1,1,1,1,1,1,1,1,13
%N A307662 Triangle T(i,j=1..i) read by rows which contain the naturally ordered divisors-or-ones of the row number i.
%C A307662 Replace 0 with 1 in A127093. - _Omar E. Pol_, Apr 21 2019
%H A307662 I. V. Serov, <a href="/A307662/b307662.txt">Rows n = 1..131 of triangle, flattened</a>
%F A307662 For j=1..floor(i/2), T(i,j)=T(i-j,j).
%F A307662 For j=floor(i/2)+1..i-1, T(i,j)=1.
%F A307662 T(i,i) = i.
%F A307662 Let i = A002024(n) and j = A002260(n):
%F A307662 a(n) = a((i-j-1)*(i-j)/2+j) if j=1..floor(i/2).
%F A307662 a(n) = 1 if j=floor(i/2)+1..i-1.
%F A307662 a(n) = i if j=i.
%F A307662 T(i,j) = a(n).
%e A307662 Triangle begins:
%e A307662   1,
%e A307662   1, 2,
%e A307662   1, 1, 3,
%e A307662   1, 2, 1, 4,
%e A307662   1, 1, 1, 1, 5,
%e A307662   1, 2, 3, 1, 1, 6,
%e A307662   1, 1, 1, 1, 1, 1, 7,
%e A307662   1, 2, 1, 4, 1, 1, 1, 8,
%e A307662   1, 1, 3, 1, 1, 1, 1, 1, 9,
%e A307662   1, 2, 1, 1, 5, 1, 1, 1, 1,10,
%e A307662   1, 1, 1, 1, 1, 1, 1, 1, 1, 1,11,
%e A307662   1, 2, 3, 4, 1, 6, 1, 1, 1, 1, 1,12,
%e A307662   ...
%t A307662 Table[Map[If[Mod[n, #] == 0, #, 1] &, Range@ n], {n, 13}] // Flatten (* _Michael De Vlieger_, Apr 23 2019 *)
%o A307662 (PARI) row(n) = vector(n, k, if ((n % k) == 0, k, 1)); \\ _Michel Marcus_, Apr 21 2019
%Y A307662 Cf. A100995, A127093, A307641, A027750, A002024, A002260.
%K A307662 nonn,tabl
%O A307662 1,3
%A A307662 _I. V. Serov_, Apr 20 2019