A109299 Primal codes of canonical finite permutations on positive integers.

1, 2, 12, 18, 360, 540, 600, 1350, 1500, 2250, 75600, 105840, 113400, 126000, 158760, 246960, 283500, 294000, 315000, 411600, 472500, 555660, 735000, 864360, 992250, 1296540, 1389150, 1440600, 1653750, 2572500, 3241350, 3601500, 3858750

Offset: 1

Author

Jon Awbrey, Jul 09 2005

Keywords

• nonn

Comments

A canonical finite permutation on positive integers is a bijective mapping of [n] = {1, ..., n} to itself, counting the empty mapping as a permutation of the empty set.

From Rémy Sigrist, Sep 18 2021: (Start)

As usual with lists, the terms of the sequence are given in ascending order.

Equivalently, these are the numbers m such that A001221(m) = A051903(m) = A061395(m) = A071625(m).

This sequence has connections with A175061; here the prime factorizations, there the run-lengths in binary expansions, encode finite permutations.

There are m! terms with m distinct prime factors, the least one being A006939(m) and the greatest one being A076954(m); these m! terms are not necessarily contiguous. (End)

Examples

			Writing (prime(i))^j as i:j, we have this table:
Primal Codes of Canonical Finite Permutations
        1 = { }
        2 = 1:1
       12 = 1:2 2:1
       18 = 1:1 2:2
      360 = 1:3 2:2 3:1
      540 = 1:2 2:3 3:1
      600 = 1:3 2:1 3:2
     1350 = 1:1 2:3 3:2
     1500 = 1:2 2:1 3:3
     2250 = 1:1 2:2 3:3
    75600 = 1:4 2:3 3:2 4:1
   105840 = 1:4 2:3 3:1 4:2
   113400 = 1:3 2:4 3:2 4:1
   126000 = 1:4 2:2 3:3 4:1
   158760 = 1:3 2:4 3:1 4:2
   246960 = 1:4 2:2 3:1 4:3
   283500 = 1:2 2:4 3:3 4:1
   294000 = 1:4 2:1 3:3 4:2
   315000 = 1:3 2:2 3:4 4:1
   411600 = 1:4 2:1 3:2 4:3
   472500 = 1:2 2:3 3:4 4:1
   555660 = 1:2 2:4 3:1 4:3
   735000 = 1:3 2:1 3:4 4:2
   864360 = 1:3 2:2 3:1 4:4
   992250 = 1:1 2:4 3:3 4:2
  1296540 = 1:2 2:3 3:1 4:4
  1389150 = 1:1 2:4 3:2 4:3
  1440600 = 1:3 2:1 3:2 4:4
  1653750 = 1:1 2:3 3:4 4:2
  2572500 = 1:2 2:1 3:4 4:3
  3241350 = 1:1 2:3 3:2 4:4
  3601500 = 1:2 2:1 3:3 4:4
  3858750 = 1:1 2:2 3:4 4:3
  5402250 = 1:1 2:2 3:3 4:4
		

References

• Suggested by Franklin T. Adams-Watters

Links

• J. Awbrey, Riffs and Rotes
• Rémy Sigrist, PARI program for A109299

Crossrefs

Cf. A001221, A006939, A051903, A061395, A071625, A076954, A106177, A108352, A108371, A109297, A109298, A109301, A175061, A347758.

Programs

PARI

\\ See Links section.

PARI

is(n) = { my (f=factor(n), p=f[,1]~, e=f[,2]~); Set(e)==[1..#e] && (#p==0 || p[#p]==prime(#p)) } \\ Rémy Sigrist, Sep 18 2021

Extensions

Offset changed to 1 and data corrected by Rémy Sigrist, Sep 18 2021