OFFSET
0,4
COMMENTS
FORMULA
EXAMPLE
The a(1) = 1 through a(3) = 10 factorizations:
2 2*6 2*6*30 2*6*30*210
2*3*6*10 6*10*30*42
2*3*6*30*70
2*5*6*30*42
2*3*10*30*42
2*3*6*10*210
2*6*10*15*42
2*6*10*21*30
2*6*14*15*30
3*6*10*14*30
2*3*5*6*10*42
2*3*5*6*14*30
2*3*6*7*10*30
2*3*6*10*14*15
The a(1) = 1 through a(3) = 14 set multipartitions:
{1} {1}{12} {1}{12}{123} {1}{12}{123}{1234}
{1}{2}{12}{13} {12}{13}{123}{124}
{1}{12}{13}{23}{124}
{1}{12}{13}{24}{123}
{1}{12}{14}{23}{123}
{1}{2}{12}{123}{134}
{1}{2}{12}{13}{1234}
{1}{2}{13}{123}{124}
{1}{3}{12}{123}{124}
{2}{12}{13}{14}{123}
{1}{2}{12}{13}{14}{23}
{1}{2}{12}{4}{13}{123}
{1}{2}{3}{12}{13}{124}
{1}{2}{3}{12}{14}{123}
MATHEMATICA
chern[n_]:=Product[Prime[i]^(n-i+1), {i, n}];
ystfac[n_]:=If[n<=1, {{}}, Join@@Table[Map[Prepend[#, d]&, Select[ystfac[n/d], Min@@#>d&]], {d, Select[Rest[Divisors[n]], SquareFreeQ]}]];
Table[Length[ystfac[chern[n]]], {n, 0, 4}]
PROG
(PARI) \\ See A318361 for count.
a(n) = {if(n==0, 1, count(vector(n, i, i)))} \\ Andrew Howroyd, Sep 01 2020
CROSSREFS
A000142 counts divisors of superprimorials.
A022915 counts permutations of the same multiset.
A103775 is the version for factorials instead of superprimorials.
A337072 is the non-strict version.
A001055 counts factorizations.
A006939 lists superprimorials or Chernoff numbers.
A045778 counts strict factorizations.
A050320 counts factorizations into squarefree numbers.
A050326 counts strict factorizations into squarefree numbers.
A050342 counts strict set multipartitions of integer partitions.
A283877 counts non-isomorphic strict set multipartitions.
A317829 counts factorizations of superprimorials.
A337069 counts strict factorizations of superprimorials.
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Aug 15 2020
EXTENSIONS
a(7)-a(13) from Andrew Howroyd, Sep 01 2020
STATUS
approved