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A131420 A tabular sequence of arrays counting ordered factorizations over least prime signatures. The unordered version is described by sequence A129306. 0
1, 2, 3, 4, 8, 13, 8, 20, 44, 75, 26, 16, 48, 132, 308, 541, 76, 176, 32, 112, 368, 1076, 2612, 4683, 208, 604, 1460, 252, 818, 64, 256, 876, 3408, 10404, 25988, 47293, 544, 1888, 5740, 14300, 768, 2316, 3172, 7880, 128, 576, 2496, 10096, 36848, 116180 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The display has 1 2 3 5 7 11 15 ... terms per column. (cf. A000041)

The arrays begin

1.....2.....4......8......16.....32.....64......128

......3.....8.....20......48....112....256......576

...........13.....44.....132....368....976.....2496

..................75.....308...1076...3408....10096

.........................541...2612..10404....36848

...............................4683..25988...116180

.....................................47293...296564

.............................................545835

..................26......76....208....544

.........................176....604...1888

...............................1460...5740

.....................................14300

................................252....768

......................................2316

................................818...3172

......................................7880

with column sums

1....5....25....173....1297....12225....124997 => A035341

Column i corresponds to partitions of i. The rows correspond successively to the partitions {i}, {i-1,1},{i-2,1,1},{i-3,1,1,1}, ..., {i-7,1,1,1,1,1,1,1}, {i-2,2}, {i-3,2,1}, {i-4,2,1,1}, {i-5,2,1,1,1}, {i-3,3}, {i-3,3,1}, {i-4,2,2}, {i-5,2,2,1}. - Roger Lipsett, Feb 26 2016

LINKS

Table of n, a(n) for n=1..50.

EXAMPLE

36 = 2*2*3*3 and is in A025487. There are 26 ways to factor 36 so a(11) = 26.

MATHEMATICA

gozinta counts ordered factorizations of an integer, and if lst is a partition we have

gozinta[1] = 1;

gozinta[n_] := gozinta[n] = 1 + Sum[gozinta[n/i], {i, Rest@Most@Divisors@n}]

a[lst_] := gozinta[Times @@ (Array[Prime, Length@lst]^lst)] (* Roger Lipsett, Feb 26 2016 *)

CROSSREFS

Cf. A000041, A000670, A002033, A025487, A035098, A035341, A050324, A074206, A095705, A098348, A104725, A108464, A129306.

Sequence in context: A238962 A238975 A098348 * A095705 A034776 A068791

Adjacent sequences:  A131417 A131418 A131419 * A131421 A131422 A131423

KEYWORD

nonn

AUTHOR

Alford Arnold, Jul 10 2007

EXTENSIONS

Corrected entries in table in comments section - Roger Lipsett, Feb 26 2016

STATUS

approved

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Last modified October 15 04:33 EDT 2019. Contains 328026 sequences. (Running on oeis4.)