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<n), for(y=x+1, n-1, for(z=y+1, n-1, if(x*y*z==n, s++))))); (6*s); }; \\ (After A122180, still quite naive) - Antti Karttunen, Jul 09 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Peter Luschny, Nov 14 2011
EXTENSIONS
Description clarified, term a(0) removed and a second example added by Antti Karttunen, Jul 09 2017
STATUS
approved