OFFSET
1,4
COMMENTS
The middle divisors of n are the divisors in the half-open interval [sqrt(n/2), sqrt(n*2)).
LINKS
Michael De Vlieger, Table of n, a(n) for n = 1..14002 (rows 1 <= n <= 10^4)
EXAMPLE
Triangle begins (rows 1..16):
1;
1;
0;
2;
0;
2, 3;
0;
2;
3;
0;
0;
3, 4;
0;
0;
3, 5;
4;
...
For n = 6 the middle divisors of 6 are 2 and 3, so row 6 is [2, 3].
For n = 7 there are no middle divisors of 7, so row 7 is [0].
For n = 8 the middle divisor of 8 is 2, so row 8 is [2].
For n = 72 the middle divisors of 72 are 6, 8 and 9, so row 72 is [6, 8, 9].
MATHEMATICA
Table[Select[Divisors@ n, Sqrt[n/2] <= # < Sqrt[2 n] &] /. {} -> {0}, {n, 80}] // Flatten (* Michael De Vlieger, Jun 14 2018 *)
PROG
(PARI) row(n) = my(v=select(x->((x >= sqrt(n/2)) && (x < sqrt(n*2))), divisors(n))); if (#v, v, [0]); \\ Michel Marcus, Aug 04 2022
CROSSREFS
KEYWORD
AUTHOR
Omar E. Pol, Jun 08 2018
STATUS
approved