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 A200214 Ordered factorizations of n with 3 distinct parts, all > 1. 4
 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 6, 0, 0, 0, 6, 0, 6, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 6, 0, 6, 0, 0, 0, 18, 0, 0, 0, 6, 0, 6, 0, 0, 0, 6, 0, 18, 0, 0, 0, 0, 0, 6, 0, 12, 0, 0, 0, 18 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,24 LINKS Antti Karttunen, Table of n, a(n) for n = 1..1001 Benny Chor, Paul Lemke, Ziv Mador, On the number of ordered factorizations of natural numbers, Discrete Mathematics, Vol. 214[1], 2000, p. 123-133. Arnold Knopfmacher and Michael Mays, Ordered and Unordered Factorizations of Integers, The Mathematica Journal, Vol 10 (1), 2006. FORMULA a(n) = 6*A122180(n). - Antti Karttunen, Jul 08 2017 EXAMPLE a(24) = 6 = card({{2,3,4}, {2,4,3}, {3,2,4}, {3,4,2}, {4,2,3}, {4,3,2}}. a(64) = 6 = card({{2,4,8}, {2,8,4}, {4,2,8}, {4,8,2}, {8,2,4}, {8,4,2}}. MATHEMATICA OrderedFactorizations[1] = {{}}; OrderedFactorizations[n_?PrimeQ] := {{n}}; OrderedFactorizations[n_] := OrderedFactorizations[n] = Flatten[Function[d, Prepend[#, d] & /@ OrderedFactorizations[n/d]] /@ Rest[Divisors[n]], 1]; a[n_] := With[{of3 = Sort /@ Select[OrderedFactorizations[n], Length[#] == 3 && Length[# // Union] == 3 &] // Union}, Length[Permutations /@ of3 // Flatten[#, 1] &]];  Table[a[n], {n, 1, 84}] (* Jean-François Alcover, Jul 02 2013, copied and adapted from The Mathematica Journal *) PROG (PARI) A200214(n) = { my(s=0); fordiv(n, x, if((x>1)&&(x

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Last modified April 22 11:46 EDT 2019. Contains 322330 sequences. (Running on oeis4.)