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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. 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

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

LINKS

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

Reinhard Zumkeller, Example for n = 120

FORMULA

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

EXAMPLE

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

PROG

(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

CROSSREFS

Cf. A058524, A060636.

Sequence in context: A069359 A318320 A014652 * A090080 A151737 A211361

Adjacent sequences:  A060445 A060446 A060447 * A060449 A060450 A060451

KEYWORD

nonn,nice

AUTHOR

Naohiro Nomoto, Apr 14 2001

STATUS

approved

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Last modified August 4 09:03 EDT 2020. Contains 336201 sequences. (Running on oeis4.)