A290095 a(n) = A275725(A060126(n)); prime factorization encodings of cycle-polynomials computed for finite permutations listed in reversed colexicographic ordering.

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

Offset: 0

Author

Antti Karttunen, Aug 17 2017

Keywords

• nonn

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.

Examples

			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].
		

Links

• Antti Karttunen, Table of n, a(n) for n = 0..40319
• Index entries for sequences related to factorial base representation

Crossrefs

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

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

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).