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A375038
Irregular triangle read by rows T(n,k), n >= 2, k >= 1, in which row n lists the nonmiddle divisors of n.
2
2, 1, 3, 1, 4, 1, 5, 1, 6, 1, 7, 1, 4, 8, 1, 9, 1, 2, 5, 10, 1, 11, 1, 2, 6, 12, 1, 13, 1, 2, 7, 14, 1, 15, 1, 2, 8, 16, 1, 17, 1, 2, 6, 9, 18, 1, 19, 1, 2, 10, 20, 1, 3, 7, 21, 1, 2, 11, 22, 1, 23, 1, 2, 3, 8, 12, 24, 1, 25, 1, 2, 13, 26, 1, 3, 9, 27, 1, 2, 14, 28
OFFSET
2,1
COMMENTS
Except the 1, all positive integers have nonmiddle divisors.
The nonmiddle divisors of n are here the divisors of n that are not in the half-open interval [sqrt(n/2), sqrt(n*2)).
LINKS
Amiram Eldar, Table of n, a(n) for n = 2..6375 (rows for n = 2..1000, flattened)
EXAMPLE
Triangle begins starting in row n = 2:
2;
1, 3;
1, 4;
1, 5;
1, 6;
1, 7;
1, 4, 8;
1, 9;
1, 2, 5, 10;
1, 11;
1, 2, 6, 12;
...
For n = 12 the divisors of 12 are [1, 2, 3, 4, 6, 12] and the middle divisors are [3, 4], so the nonmiddle divisors are [1, 2, 6, 12], the same as the row n = 12 of the triangle.
MATHEMATICA
row[n_] := Select[Divisors[n], !(Sqrt[n/2] <= # < Sqrt[2*n]) &]; Table[row[n], {n, 2, 28}] // Flatten (* Amiram Eldar, Jul 29 2024 *)
CROSSREFS
Nonzero terms of A375037.
The sum of row n is A302433(n).
The number of terms in row n is A067743(n).
Column 1 gives A054977.
Sequence in context: A228179 A322313 A322315 * A319338 A177815 A007879
KEYWORD
nonn,tabf,easy,look
AUTHOR
Omar E. Pol, Jul 28 2024
STATUS
approved