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A109297 Primal codes of finite permutations on positive integers. 12
1, 2, 9, 12, 18, 40, 112, 125, 250, 352, 360, 540, 600, 675, 832, 1008, 1125, 1350, 1500, 2176, 2250, 2268, 2352, 2401, 3168, 3969, 4802, 4864, 7488, 7938, 10692, 11616, 11776, 14000, 19584, 21609, 27440, 28812, 29403, 29696, 32448, 35000, 37908, 43218, 43776 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

A finite permutation is a bijective mapping from a finite set to itself, counting the empty mapping as a permutation of the empty set.

Also Heinz numbers of integer partitions where the set of distinct parts is equal to the set of distinct multiplicities. These partitions are counted by A114640. The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k). - Gus Wiseman, Apr 02 2019

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..100

J. Awbrey, Riffs and Rotes

EXAMPLE

Writing (prime(i))^j as i:j, we have the following table:

Primal Codes of Finite Permutations on Positive Integers

` ` ` 1 = { }

` ` ` 2 = 1:1

` ` ` 9 = 2:2

` ` `12 = 1:2 2:1

` ` `18 = 1:1 2:2

` ` `40 = 1:3 3:1

` ` 112 = 1:4 4:1

` ` 125 = 3:3

` ` 250 = 1:1 3:3

` ` 352 = 1:5 5:1

` ` 360 = 1:3 2:2 3:1

` ` 540 = 1:2 2:3 3:1

` ` 600 = 1:3 2:1 3:2

` ` 675 = 2:3 3:2

` ` 832 = 1:6 6:1

` `1008 = 1:4 2:2 4:1

` `1125 = 2:2 3:3

` `1350 = 1:1 2:3 3:2

` `1500 = 1:2 2:1 3:3

` `2176 = 1:7 7:1

` `2250 = 1:1 2:2 3:3

MAPLE

a:= proc(n) option remember; local k; for k from 1+`if`(n=1, 0,

      a(n-1)) while (l-> sort(map(i-> i[2], l)) <> sort(map(

      i-> numtheory[pi](i[1]), l)))(ifactors(k)[2]) do od; k

    end:

seq(a(n), n=1..45);  # Alois P. Heinz, Mar 08 2019

MATHEMATICA

Select[Range[1000], #==1||Union[PrimePi/@First/@FactorInteger[#]]==Union[Last/@FactorInteger[#]]&] (* Gus Wiseman, Apr 02 2019 *)

CROSSREFS

Cf. A076954, A106177, A108352, A108371, A109298, A109301, A056239, A112798, A114640, A118914.

Cf. A324524, A324525, A324571, A325127, A325128, A325130, A325131.

Sequence in context: A225547 A325755 A324570 * A048768 A070226 A273669

Adjacent sequences:  A109294 A109295 A109296 * A109298 A109299 A109300

KEYWORD

nonn

AUTHOR

Jon Awbrey, Jul 08 2005

EXTENSIONS

More terms from Franklin T. Adams-Watters, Dec 19 2005

Offset set to 1 by Alois P. Heinz, Mar 08 2019

STATUS

approved

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Last modified August 1 06:45 EDT 2021. Contains 346384 sequences. (Running on oeis4.)