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A299761
Irregular triangle read by rows: T(n,k), n >= 1, k >= 1, in which row n lists the middle divisors of n, or 0 if there are no middle divisors of n.
24
1, 1, 0, 2, 0, 2, 3, 0, 2, 3, 0, 0, 3, 4, 0, 0, 3, 5, 4, 0, 3, 0, 4, 5, 0, 0, 0, 4, 6, 5, 0, 0, 4, 7, 0, 5, 6, 0, 4, 0, 0, 5, 7, 6, 0, 0, 0, 5, 8, 0, 6, 7, 0, 0, 5, 9, 0, 0, 6, 8, 7, 5, 0, 0, 0, 6, 9, 0, 7, 8, 0, 0, 0, 6, 10, 0, 0, 7, 9, 8, 0, 6, 11, 0, 0, 0, 7, 10, 0, 6, 8, 9, 0, 0, 0, 0, 7, 11, 0, 0, 8, 10
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
Row sums give A071090.
The number of nonzero terms in row n is A067742(n).
Nonzero terms give A303297.
Indices of the rows where there are zeros give A071561.
Indices of the rows where there are nonzero terms give A071562.
Sequence in context: A209689 A204329 A111565 * A141099 A127710 A137510
KEYWORD
nonn,tabf,look
AUTHOR
Omar E. Pol, Jun 08 2018
STATUS
approved