A109297 Primal codes of finite permutations on positive integers.

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

Offset: 1

Author

Jon Awbrey, Jul 08 2005

Keywords

• nonn

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

Examples

			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
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..300 (terms 1..100 from Alois P. Heinz)
• Jon Awbrey, Riffs and Rotes.

Crossrefs

Subsequence of A130091.

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

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

Programs

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 *)

PARI

is(n) = {my(f = factor(n), p = f[,1], e = vecsort(f[,2])); for(i=1, #p, if(primepi(p[i]) != e[i], return(0))); 1}; \\ Amiram Eldar, Jul 30 2022

Extensions

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

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