A109299 - OEIS

%I #11 Sep 18 2021 07:06:50

%S 1,2,12,18,360,540,600,1350,1500,2250,75600,105840,113400,126000,

%T 158760,246960,283500,294000,315000,411600,472500,555660,735000,

%U 864360,992250,1296540,1389150,1440600,1653750,2572500,3241350,3601500,3858750

%N Primal codes of canonical finite permutations on positive integers.

%C 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.

%C From _Rémy Sigrist_, Sep 18 2021: (Begin)

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

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

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

%C 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.

%C (End)

%D Suggested by Franklin T. Adams-Watters

%H J. Awbrey, <a href="https://oeis.org/wiki/Riffs_and_Rotes">Riffs and Rotes</a>

%H Rémy Sigrist, <a href="/A109299/a109299.gp.txt">PARI program for A109299</a>

%e Writing (prime(i))^j as i:j, we have this table:

%e Primal Codes of Canonical Finite Permutations

%e ` ` ` 1 = { }

%e ` ` ` 2 = 1:1

%e ` ` `12 = 1:2 2:1

%e ` ` `18 = 1:1 2:2

%e ` ` 360 = 1:3 2:2 3:1

%e ` ` 540 = 1:2 2:3 3:1

%e ` ` 600 = 1:3 2:1 3:2

%e ` `1350 = 1:1 2:3 3:2

%e ` `1500 = 1:2 2:1 3:3

%e ` `2250 = 1:1 2:2 3:3

%e ` 75600 = 1:4 2:3 3:2 4:1

%e `105840 = 1:4 2:3 3:1 4:2

%e `113400 = 1:3 2:4 3:2 4:1

%e `126000 = 1:4 2:2 3:3 4:1

%e `158760 = 1:3 2:4 3:1 4:2

%e `246960 = 1:4 2:2 3:1 4:3

%e `283500 = 1:2 2:4 3:3 4:1

%e `294000 = 1:4 2:1 3:3 4:2

%e `315000 = 1:3 2:2 3:4 4:1

%e `411600 = 1:4 2:1 3:2 4:3

%e `472500 = 1:2 2:3 3:4 4:1

%e `555660 = 1:2 2:4 3:1 4:3

%e `735000 = 1:3 2:1 3:4 4:2

%e `864360 = 1:3 2:2 3:1 4:4

%e `992250 = 1:1 2:4 3:3 4:2

%e 1296540 = 1:2 2:3 3:1 4:4

%e 1389150 = 1:1 2:4 3:2 4:3

%e 1440600 = 1:3 2:1 3:2 4:4

%e 1653750 = 1:1 2:3 3:4 4:2

%e 2572500 = 1:2 2:1 3:4 4:3

%e 3241350 = 1:1 2:3 3:2 4:4

%e 3601500 = 1:2 2:1 3:3 4:4

%e 3858750 = 1:1 2:2 3:4 4:3

%e 5402250 = 1:1 2:2 3:3 4:4

%o (PARI) See Links section.

%o (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

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

%K nonn

%O 1,2

%A _Jon Awbrey_, Jul 09 2005

%E Offset changed to 1 and data corrected by _Rémy Sigrist_, Sep 18 2021