A208460 Triangle read by rows: T(n,k) = n minus the k-th proper divisor of n.

1, 2, 3, 2, 4, 5, 4, 3, 6, 7, 6, 4, 8, 6, 9, 8, 5, 10, 11, 10, 9, 8, 6, 12, 13, 12, 7, 14, 12, 10, 15, 14, 12, 8, 16, 17, 16, 15, 12, 9, 18, 19, 18, 16, 15, 10, 20, 18, 14, 21, 20, 11, 22, 23, 22, 21, 20, 18, 16, 12, 24, 20, 25, 24, 13, 26, 24, 18, 27, 26, 24

Offset

2,2

Comments

Conjecture: one of the divisors of T(n,k) is also the k-th divisor of n. In a diagram of the structure of divisors of the natural numbers (see link) the mentioned divisors of the elements of row n are located on a straight line to 45 degrees from the vertical straight line that contains the divisors of n, therefore the divisors of n are predictable.

Links

Alois P. Heinz, Rows n = 2..1540, flattened

Omar E. Pol, Illustration of the structure of divisors of the natural numbers, for n = 1..16

Formula

T(n,k) = n - A027751(n,k).

Example

Written as a triangle starting from n = 2:
1;
2;
3, 2;
4;
5, 4, 3;
6;
7, 6, 4;
8, 6;
9, 8, 5;
10;
11, 10, 9, 8, 6;
12;

Maple

with (numtheory):
T:= n-> map(x-> n-x, sort([(divisors(n) minus {n})[]]))[]:
seq (T(n), n=2..50); # Alois P. Heinz, Apr 11 2012

Mathematica

T[n_] := Most[n-Divisors[n]]; Table[T[n], {n, 2, 50}] // Flatten (* Jean-François Alcover, Feb 21 2017 *)

Crossrefs

Column 1 is A000027. Row n has length A032741(n). Row sums give the positives A094471. Right border is A060681.

Cf. A000005, A027750, A027751.

Sequence in context: A026358 A304098 A239690 * A343934 A119465 A359369

Adjacent sequences: A208457 A208458 A208459 * A208461 A208462 A208463

Keyword

nonn,tabf

Author

Omar E. Pol, Feb 28 2012

Status

approved