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 A007359 Number of partitions of n into pairwise coprime parts that are >= 2. (Formerly M0143) 56
 1, 0, 1, 1, 1, 2, 1, 3, 2, 3, 3, 5, 4, 6, 5, 5, 8, 9, 10, 11, 11, 10, 14, 18, 19, 18, 20, 20, 25, 30, 35, 34, 32, 32, 43, 43, 57, 56, 51, 55, 67, 78, 87, 87, 80, 82, 97, 125, 128, 127, 128, 127, 146, 182, 191, 185, 184, 193, 213, 263, 290, 279, 258, 271, 312, 354, 404, 402 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 COMMENTS This sequence is of interest for group theory. The partitions counted by a(n) correspond to conjugacy classes of optimal order of the symmetric group of n elements: they have no fixed point, their order is the direct product of their cycle lengths and they are not contained in a subgroup of Sym_p for p < n. A123131 gives the maximum order (LCM) reachable by these partitions. REFERENCES N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Fausto A. C. Cariboni, Table of n, a(n) for n = 0..750 (terms 0..400 from Alois P. Heinz) M. LeBrun & D. Hoey, Emails FORMULA a(n) = A051424(n) - A051424(n-1). - Vladeta Jovovic, Dec 11 2004 EXAMPLE The a(17) = 9 strict partitions into pairwise coprime parts that are greater than 1 are (17), (15,2), (14,3), (13,4), (12,5), (11,6), (10,7), (9,8), (7,5,3,2). - Gus Wiseman, Apr 14 2018 MAPLE with(numtheory): b:= proc(n, i, s) option remember; local f;       if n=0 then 1     elif i<2 then 0     else f:= factorset(i);          b(n, i-1, select(x-> is(x is(x b(n, n, {}): seq(a(n), n=0..80);  # Alois P. Heinz, Mar 14 2012 MATHEMATICA b[n_, i_, s_] := b[n, i, s] = Module[{f}, If[n == 0 || i == 1, 1, If[i<2, 0, f = FactorInteger[i][[All, 1]]; b[n, i-1, Select[s, #

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Last modified April 17 08:34 EDT 2021. Contains 343064 sequences. (Running on oeis4.)