

A208460


Triangle read by rows: T(n,k) = n minus the kth 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
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OFFSET

2,2


COMMENTS

Conjecture: one of the divisors of T(n,k) is also the kth 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> nx, sort([(divisors(n) minus {n})[]]))[]:
seq (T(n), n=2..50); # Alois P. Heinz, Apr 11 2012


MATHEMATICA

T[n_] := Most[nDivisors[n]]; Table[T[n], {n, 2, 50}] // Flatten (* JeanFrançois 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



