A210959 Triangle read by rows in which row n lists the divisors of n starting with 1, n, the second smallest divisor of n, the second largest divisor of n, the third smallest divisor of n, the third largest divisor of n, and so on.

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

Offset: 1

Author

Omar E. Pol, Jul 29 2012

Keywords

• nonn
• tabf

Comments

A two-dimensional arrangement of squares has the property that the number of vertices in row n equals the number of divisors of n. So T(n,k) is represented in the structure as the k-th vertex of row n (see the illustration of initial terms).

Examples

			Written as an irregular triangle the sequence begins:
1;
1, 2;
1, 3;
1, 4, 2;
1, 5;
1, 6, 2, 3;
1, 7;
1, 8, 2, 4;
1, 9, 3;
1, 10, 2, 5;
1, 11;
1, 12, 2, 6, 3, 4;
		

Links

• Michel Marcus, Rows 1..1000, flattened
• Omar E. Pol, Illustration of initial terms
• Index entries for sequences related to sigma(n)

Crossrefs

Row n has length A000005(n). Row sums give A000203. Right border gives A033677.

Cf. A027750, A161901, A212119.

Programs

PARI

row(n) = my(d=divisors(n)); vector(#d, k, if (k % 2, d[(k+1)/2], d[#d-k/2+1])); \\ Michel Marcus, Jun 20 2019