A081514 Triangle read by rows: row n = lexicographically earliest choice for n distinct divisors of A081512(n) = m whose sum is m.

1, 0, 0, 1, 2, 3, 1, 2, 3, 6, 1, 2, 3, 6, 12, 1, 2, 3, 4, 6, 8, 1, 2, 3, 4, 6, 8, 24, 1, 2, 3, 4, 5, 10, 15, 20, 1, 2, 3, 4, 6, 7, 12, 21, 28, 1, 2, 3, 4, 5, 6, 15, 20, 24, 40, 1, 2, 3, 4, 5, 6, 8, 12, 15, 24, 40, 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 24, 30, 1, 2, 3, 4, 5, 6, 9, 10, 12, 18, 20, 30, 60

Offset: 1

Author

Amarnath Murthy, Mar 27 2003

Keywords

• nonn
• tabl

Comments

A081512(n) = smallest number m which can be expressed as the sum of n of its distinct divisors, or 0 if no such number exists. (n=2 is the only time A081512(n) = 0.)

Look at all sets of n distinct divisors d_1, ..., d_n of m = A081512(n) such that d_1+...+d_n = m, and choose the lexicographically earliest solution. That is row n of the current triangle.

The value of d_n in the lexicographically earliest solution is given in A081513.

Examples

			The lexicographically earliest solutions are:
[1]
[0, 0]
[1, 2, 3]
[1, 2, 3, 6]
[1, 2, 3, 6, 12]
[1, 2, 3, 4, 6, 8]
[1, 2, 3, 4, 6, 8, 24]
[1, 2, 3, 4, 5, 10, 15, 20]
[1, 2, 3, 4, 6, 7, 12, 21, 28]
[1, 2, 3, 4, 5, 6, 15, 20, 24, 40]
[1, 2, 3, 4, 5, 6, 8, 12, 15, 24, 40]
[1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 24, 30]
[1, 2, 3, 4, 5, 6, 9, 10, 12, 18, 20, 30, 60]
...
		

Links

• David A. Corneth, Table of n, a(n) for n = 1..10296

Crossrefs

Cf. A081512, A081513.

Extensions

Corrected by Caleb M. Shor (cshor(AT)bates.edu), Sep 26 2007

Edited by N. J. A. Sloane, May 24 2020 at the suggestion of Jinyuan Wang, who also gave the first 13 rows.