cp's OEIS Frontend

A337073 Number of strict factorizations of the superprimorial A006939(n) into squarefree numbers > 1.

%I A337073 #10 Sep 05 2020 03:42:54
%S A337073 1,1,1,2,14,422,59433,43181280,178025660042,4550598470020490,
%T A337073 782250333882971717562,974196106965358319940100513,
%U A337073 9412280190038329162111356578977100,751537739224674099813783040471383322758327
%N A337073 Number of strict factorizations of the superprimorial A006939(n) into squarefree numbers > 1.
%C A337073 The n-th superprimorial is A006939(n) = Product_{i = 1..n} prime(i)^(n - i + 1). It has n! divisors.
%C A337073 Also the number of strict set multipartitions (sets of sets) of the multiset of prime factors of the superprimorial A006939(n).
%F A337073 a(n) = A050326(A006939(n)).
%F A337073 a(n) = A318361(A002110(n)). - _Andrew Howroyd_, Sep 01 2020
%e A337073 The a(1) = 1 through a(3) = 10 factorizations:
%e A337073     2  2*6  2*6*30    2*6*30*210
%e A337073             2*3*6*10  6*10*30*42
%e A337073                       2*3*6*30*70
%e A337073                       2*5*6*30*42
%e A337073                       2*3*10*30*42
%e A337073                       2*3*6*10*210
%e A337073                       2*6*10*15*42
%e A337073                       2*6*10*21*30
%e A337073                       2*6*14*15*30
%e A337073                       3*6*10*14*30
%e A337073                       2*3*5*6*10*42
%e A337073                       2*3*5*6*14*30
%e A337073                       2*3*6*7*10*30
%e A337073                       2*3*6*10*14*15
%e A337073 The a(1) = 1 through a(3) = 14 set multipartitions:
%e A337073     {1}  {1}{12}  {1}{12}{123}    {1}{12}{123}{1234}
%e A337073                   {1}{2}{12}{13}  {12}{13}{123}{124}
%e A337073                                   {1}{12}{13}{23}{124}
%e A337073                                   {1}{12}{13}{24}{123}
%e A337073                                   {1}{12}{14}{23}{123}
%e A337073                                   {1}{2}{12}{123}{134}
%e A337073                                   {1}{2}{12}{13}{1234}
%e A337073                                   {1}{2}{13}{123}{124}
%e A337073                                   {1}{3}{12}{123}{124}
%e A337073                                   {2}{12}{13}{14}{123}
%e A337073                                   {1}{2}{12}{13}{14}{23}
%e A337073                                   {1}{2}{12}{4}{13}{123}
%e A337073                                   {1}{2}{3}{12}{13}{124}
%e A337073                                   {1}{2}{3}{12}{14}{123}
%t A337073 chern[n_]:=Product[Prime[i]^(n-i+1),{i,n}];
%t A337073 ystfac[n_]:=If[n<=1,{{}},Join@@Table[Map[Prepend[#,d]&,Select[ystfac[n/d],Min@@#>d&]],{d,Select[Rest[Divisors[n]],SquareFreeQ]}]];
%t A337073 Table[Length[ystfac[chern[n]]],{n,0,4}]
%o A337073 (PARI) \\ See A318361 for count.
%o A337073 a(n) = {if(n==0, 1, count(vector(n, i, i)))} \\ _Andrew Howroyd_, Sep 01 2020
%Y A337073 A000142 counts divisors of superprimorials.
%Y A337073 A022915 counts permutations of the same multiset.
%Y A337073 A103775 is the version for factorials instead of superprimorials.
%Y A337073 A337072 is the non-strict version.
%Y A337073 A001055 counts factorizations.
%Y A337073 A006939 lists superprimorials or Chernoff numbers.
%Y A337073 A045778 counts strict factorizations.
%Y A337073 A050320 counts factorizations into squarefree numbers.
%Y A337073 A050326 counts strict factorizations into squarefree numbers.
%Y A337073 A050342 counts strict set multipartitions of integer partitions.
%Y A337073 A076954 can be used instead of A006939 (cf. A307895, A325337).
%Y A337073 A283877 counts non-isomorphic strict set multipartitions.
%Y A337073 A317829 counts factorizations of superprimorials.
%Y A337073 A337069 counts strict factorizations of superprimorials.
%Y A337073 Cf. A000178, A002110, A022559, A103774, A124010, A181818, A318361, A336417, A337070.
%K A337073 nonn,more
%O A337073 0,4
%A A337073 _Gus Wiseman_, Aug 15 2020
%E A337073 a(7)-a(13) from _Andrew Howroyd_, Sep 01 2020