A060448 Each c(i) is "multiply" (*) or "divide" (/); d(1) = 1 < d(2) < ... < d(m) = n are the divisors of n; a(n) is number of choices for c(1), ..., c(m-1) so that d(1) c(1) d(2) c(2) d(3), .., c(m-1) d(m) is an integer.

1, 1, 1, 2, 1, 5, 1, 5, 2, 5, 1, 13, 1, 5, 5, 9, 1, 13, 1, 13, 5, 5, 1, 62, 2, 5, 5, 13, 1, 59, 1, 16, 5, 5, 5, 90, 1, 5, 5, 62, 1, 59, 1, 13, 13, 5, 1, 192, 2, 13, 5, 13, 1, 62, 5, 62, 5, 5, 1, 817, 1, 5, 13, 32, 5, 59, 1, 13, 5, 59, 1, 885, 1, 5, 13, 13, 5, 59, 1, 192, 9, 5, 1, 817, 5, 5

Offset: 1

Author

Naohiro Nomoto, Apr 14 2001

Keywords

• nonn
• nice

Comments

a(n) = number of partitions of the set of divisors of n into two subsets U and V such that min(U) < min(V) and product(V) divides product(U). [Reinhard Zumkeller, Apr 05 2012]

It would appear that a(n) depends only on n's prime signature. - Charlie Neder, Oct 02 2018

Examples

			For n = 6 there are 5 possibilities: 1*2*3*6=36, 1/2*3*6=9, 1*2/3*6=4, 1/2/3*6=1, 1*2*3/6=1 For n = 18 there are 13 possibilities: 1*2*3*6*9*18 1/2*3*6*9*18 1*2/3*6*9*18 1*2*3/6*9*18 1*2*3*6/9*18 1*2*3*6*9/18 1/2/3*6*9*18 1/2/3*6/9*18 1/2*3*6/9*18 1*2/3/6*9*18 1*2/3*6/9*18 1*2/3*6*9/18 1*2*3/6/9*18
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..1000
• Reinhard Zumkeller, Example for n = 120

Crossrefs

Cf. A058524, A060636.

Programs

Haskell

import Data.List (subsequences, (\\))
a060448 n = length [us | let ds = a027750_row n,
                         us <- init $ tail $ subsequences ds,
                         let vs = ds \\ us, head us < head vs,
                         product us `mod` product vs == 0] + 1
-- Reinhard Zumkeller, Apr 05 2012

Formula

a(A008578(n)) = 1; a(A002808(n)) > 1. [Reinhard Zumkeller, Apr 05 2012]