cp's OEIS Frontend

A337069 Number of strict factorizations of the superprimorial A006939(n).

%I A337069 #15 Sep 05 2020 03:42:39
%S A337069 1,1,3,34,1591,360144,442349835,3255845551937,156795416820025934,
%T A337069 53452979022001011490033,138542156296245533221812350867,
%U A337069 2914321438328993304235584538307144802,528454951438415221505169213611461783474874149,873544754831735539240447436467067438924478174290477803
%N A337069 Number of strict factorizations of the superprimorial A006939(n).
%C A337069 The n-th superprimorial is A006939(n) = Product_{i = 1..n} prime(i)^(n - i + 1).
%C A337069 Also the number of strict multiset partitions of  {1,2,2,3,3,3,...,n}, a multiset with i copies of i for i = 1..n.
%F A337069 a(n) = A045778(A006939(n)).
%F A337069 a(n) = A318286(A002110(n)). - _Andrew Howroyd_, Sep 01 2020
%e A337069 The a(3) = 34 factorizations:
%e A337069   2*3*4*15  2*3*60   2*180  360
%e A337069   2*3*5*12  2*4*45   3*120
%e A337069   2*3*6*10  2*5*36   4*90
%e A337069   2*4*5*9   2*6*30   5*72
%e A337069   3*4*5*6   2*9*20   6*60
%e A337069             2*10*18  8*45
%e A337069             2*12*15  9*40
%e A337069             3*4*30   10*36
%e A337069             3*5*24   12*30
%e A337069             3*6*20   15*24
%e A337069             3*8*15   18*20
%e A337069             3*10*12
%e A337069             4*5*18
%e A337069             4*6*15
%e A337069             4*9*10
%e A337069             5*6*12
%e A337069             5*8*9
%t A337069 chern[n_]:=Product[Prime[i]^(n-i+1),{i,n}];
%t A337069 stfa[n_]:=If[n<=1,{{}},Join@@Table[Map[Prepend[#,d]&,Select[stfa[n/d],Min@@#>d&]],{d,Rest[Divisors[n]]}]];
%t A337069 Table[Length[stfa[chern[n]]],{n,0,3}]
%o A337069 (PARI) \\ See A318286 for count.
%o A337069 a(n) = {if(n==0, 1, count(vector(n, i, i)))} \\ _Andrew Howroyd_, Sep 01 2020
%Y A337069 A022915 counts permutations of the same multiset.
%Y A337069 A157612 is the version for factorials instead of superprimorials.
%Y A337069 A317829 is the non-strict version.
%Y A337069 A337072 is the non-strict version with squarefree factors.
%Y A337069 A337073 is the case with squarefree factors.
%Y A337069 A000217 counts prime factors (with multiplicity) of superprimorials.
%Y A337069 A001055 counts factorizations.
%Y A337069 A006939 lists superprimorials or Chernoff numbers.
%Y A337069 A045778 counts strict factorizations.
%Y A337069 A076954 can be used instead of A006939 (cf. A307895, A325337).
%Y A337069 A181818 lists products of superprimorials, with complement A336426.
%Y A337069 A322583 counts factorizations into factorials.
%Y A337069 Cf. A000142, A000178, A002110, A022559, A027423, A303279, A318286, A322583, A337070, A337071.
%K A337069 nonn
%O A337069 0,3
%A A337069 _Gus Wiseman_, Aug 15 2020
%E A337069 a(7)-a(13) from _Andrew Howroyd_, Sep 01 2020