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
Amiram Eldar, Table of n, a(n) for n = 1..300 (terms 1..100 from Alois P. Heinz)
Jon 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 *)
PROG
(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
CROSSREFS
Subsequence of A130091.
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