A275725 a(n) = A275723(A002110(1+A084558(n)), n); prime factorization encodings of cycle-polynomials computed for finite permutations listed in the order that is used in tables A060117 / A060118.
2, 4, 18, 8, 12, 8, 150, 100, 54, 16, 24, 16, 90, 40, 54, 16, 36, 16, 60, 40, 36, 16, 24, 16, 1470, 980, 882, 392, 588, 392, 750, 500, 162, 32, 48, 32, 270, 80, 162, 32, 108, 32, 120, 80, 72, 32, 48, 32, 1050, 700, 378, 112, 168, 112, 750, 500, 162, 32, 48, 32, 450, 200, 162, 32, 72, 32, 300, 200, 108, 32, 48, 32, 630, 280, 378, 112, 252, 112, 450, 200
Offset: 0
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Consider the first eight permutations (indices 0-7) listed in A060117: 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] 3,2,1 [One transposition jumping over a fixed element, a(4) = 2^2 * 3^1 = 12] 2,3,1 [One 3-cycle, thus a(5) = 2^3 = 8] 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] and also the seventeenth one at n=16 [A007623(16)=220] where we have: 3,4,1,2 [Two 2-cycles crossed, thus a(16) = 2^2 * 3^2 = 36].
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