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

1,5

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.

Links

Table of n, a(n) for n=1..91.

Example

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]
...

Crossrefs

Cf. A081512, A081513.

Sequence in context: A167157 A238837 A309940 * A109206 A292746 A176506

Adjacent sequences: A081511 A081512 A081513 * A081515 A081516 A081517

Keyword

nonn,tabl

Author

Amarnath Murthy, Mar 27 2003

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.

Status

approved