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 A109299 Primal codes of canonical finite permutations on positive integers. 2
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified May 30 12:57 EDT 2023. Contains 363050 sequences. (Running on oeis4.)