OFFSET
0,3
COMMENTS
Number of factorizations of the superprimorial A006939(n) into factors > 1. - Gus Wiseman, Aug 21 2020
FORMULA
EXAMPLE
For n = 2 we have a multiset {1, 2, 2} which can be partitioned as {{1}, {2}, {2}} or {{1, 2}, {2}} or {{1}, {2, 2}} or {{1, 2, 2}}, thus a(2) = 4.
MAPLE
g:= proc(n, k) option remember; uses numtheory; `if`(n>k, 0, 1)+
`if`(isprime(n), 0, add(`if`(d>k or max(factorset(n/d))>d, 0,
g(n/d, d)), d=divisors(n) minus {1, n}))
end:
a:= n-> g(mul(ithprime(i)^i, i=1..n)$2):
seq(a(n), n=0..5); # Alois P. Heinz, Jul 26 2020
MATHEMATICA
chern[n_]:=Product[Prime[i]^(n-i+1), {i, n}];
facs[n_]:=If[n<=1, {{}}, Join@@Table[Map[Prepend[#, d]&, Select[facs[n/d], Min@@#>=d&]], {d, Rest[Divisors[n]]}]];
Table[Length[facs[chern[n]]], {n, 3}] (* Gus Wiseman, Aug 21 2020 *)
PROG
(PARI) \\ See A318284 for count.
a(n) = {if(n==0, 1, count(vector(n, i, i)))} \\ Andrew Howroyd, Aug 31 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, Aug 10 2018
EXTENSIONS
a(0)=1 prepended and a(7) added by Alois P. Heinz, Jul 26 2020
a(8)-a(13) from Andrew Howroyd, Aug 31 2020
STATUS
approved