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

1,2

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: (Begin)

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)

References

Suggested by Franklin T. Adams-Watters

Links

Table of n, a(n) for n=1..33.

J. Awbrey, Riffs and Rotes

Rémy Sigrist, PARI program for A109299

Example

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

Prog

(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

Crossrefs

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

Sequence in context: A101074 A115109 A048001 * A216629 A337290 A259409

Adjacent sequences: A109296 A109297 A109298 * A109300 A109301 A109302

Keyword

nonn

Author

Jon Awbrey, Jul 09 2005

Extensions

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

Status

approved