OFFSET
1,2
COMMENTS
A strict factorization of n is a set of distinct positive integers > 1 with product n.
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
EXAMPLE
The a(1) = 1 through a(12) = 9 factorizations:
() () () () () () () () () () () ()
(2) (3) (2) (5) (2) (7) (2) (3) (2) (11) (2)
(4) (3) (4) (9) (5) (3)
(6) (8) (10) (4)
(2*3) (2*4) (2*5) (6)
(12)
(2*3)
(2*6)
(3*4)
MAPLE
sf1:= proc(n, m)
local D, d;
if n = 1 then return 1 fi;
D:= select(`<`, numtheory:-divisors(n) minus {1}, m);
add( procname(n/d, d), d= D)
end proc:
sf:= proc(n) option remember; sf1(n, n+1) end proc:f:= proc(n) local d; add(sf(d), d=numtheory:-divisors(n)) end proc:map(f, [$1..100]); # Robert Israel, Mar 10 2021
MATHEMATICA
facs[n_]:=If[n<=1, {{}}, Join@@Table[Map[Prepend[#, d]&, Select[facs[n/d], Min@@#>=d&]], {d, Rest[Divisors[n]]}]];
Table[Sum[Length[Select[facs[k], UnsameQ@@#&]], {k, Divisors[n]}], {n, 30}]
CROSSREFS
A version for partitions is A026906 (strict partitions of 1..n).
A version for partitions is A036469 (strict partitions of 0..n).
A version for partitions is A047966 (strict partitions of divisors).
The non-strict version is A057567.
A000009 counts strict partitions.
A001222 counts prime-power divisors.
A005117 lists squarefree numbers.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 05 2021
STATUS
approved