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A208460 Triangle read by rows: T(n,k) = n minus the k-th proper divisor of n. 1
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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 A090321

Adjacent sequences:  A208457 A208458 A208459 * A208461 A208462 A208463

KEYWORD

nonn,tabf

AUTHOR

Omar E. Pol, Feb 28 2012

STATUS

approved

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Last modified August 2 01:19 EDT 2021. Contains 346408 sequences. (Running on oeis4.)