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A290095 a(n) = A275725(A060126(n)); prime factorization encodings of cycle-polynomials computed for finite permutations listed in reversed colexicographic ordering. 8
2, 4, 18, 8, 8, 12, 150, 100, 54, 16, 16, 24, 54, 16, 90, 40, 36, 16, 16, 24, 40, 60, 16, 36, 1470, 980, 882, 392, 392, 588, 750, 500, 162, 32, 32, 48, 162, 32, 270, 80, 108, 32, 32, 48, 80, 120, 32, 72, 750, 500, 162, 32, 32, 48, 1050, 700, 378, 112, 112, 168, 450, 200, 162, 32, 32, 72, 200, 300, 32, 48, 108, 32, 162, 32, 270, 80, 108, 32, 378, 112, 630, 280 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

In this context "cycle-polynomials" are single-variable polynomials where the coefficients (encoded with the exponents of prime factorization of n) are equal to the lengths of cycles in the permutation listed with index n in table A055089 (A195663). See the examples.

LINKS

Antti Karttunen, Table of n, a(n) for n = 0..40319

Index entries for sequences related to factorial base representation

FORMULA

a(n) = A275725(A060126(n)).

Other identities:

A046523(a(n)) = A290096(n).

A056170(a(n)) = A055090(n).

A046660(a(n)) = A055091(n).

A072411(a(n)) = A055092(n).

A275812(a(n)) = A055093(n).

EXAMPLE

Consider the first eight permutations (indices 0-7) listed in A055089:

  1 [Only the first 1-cycle explicitly listed thus a(0) = 2^1 = 2]

  2,1 [One transposition (2-cycle) in beginning, thus a(1) = 2^2 = 4]

  1,3,2 [One fixed element in beginning, then transposition, thus a(2) = 2^1 * 3^2 = 18]

  3,1,2 [One 3-cycle, thus a(3) = 2^3 = 8]

  2,3,1 [One 3-cycle, thus a(4) = 2^3 = 8]

  3,2,1 [One transposition jumping over a fixed element, a(5) = 2^2 * 3^1 = 12]

  1,2,4,3 [Two 1-cycles, then a 2-cycle, thus a(6) = 2^1 * 3^1 * 5^2 = 150].

  2,1,4,3 [Two 2-cycles, not crossed, thus a(7) = 2^2 * 5^2 = 100].

CROSSREFS

Cf. A055090, A055091, A055092, A055093, A060126, A290096, A290097.

Cf. also A275725, A275734, A275735, A276076 and tables A055089, A195663.

Sequence in context: A136147 A275837 A119510 * A275725 A242528 A137933

Adjacent sequences:  A290092 A290093 A290094 * A290096 A290097 A290098

KEYWORD

nonn

AUTHOR

Antti Karttunen, Aug 17 2017

STATUS

approved

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Last modified January 15 23:42 EST 2019. Contains 319184 sequences. (Running on oeis4.)