|
|
A323086
|
|
Number of factorizations of n into factors > 1 such that no factor is a power of any other (unequal) factor.
|
|
1
|
|
|
1, 1, 1, 2, 1, 2, 1, 2, 2, 2, 1, 4, 1, 2, 2, 3, 1, 4, 1, 4, 2, 2, 1, 6, 2, 2, 2, 4, 1, 5, 1, 3, 2, 2, 2, 9, 1, 2, 2, 6, 1, 5, 1, 4, 4, 2, 1, 9, 2, 4, 2, 4, 1, 6, 2, 6, 2, 2, 1, 11, 1, 2, 4, 4, 2, 5, 1, 4, 2, 5, 1, 14, 1, 2, 4, 4, 2, 5, 1, 9, 3, 2, 1, 11, 2, 2
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,4
|
|
LINKS
|
|
|
EXAMPLE
|
The a(72) = 14 factorizations:
(2*2*2*3*3),
(2*2*2*9), (2*2*3*6),
(2*2*18), (2*3*12), (2*6*6), (3*3*8), (3*4*6),
(2*36), (3*24), (4*18), (6*12), (8*9),
(72).
|
|
MATHEMATICA
|
facs[n_]:=If[n<=1, {{}}, Join@@Table[Map[Prepend[#, d]&, Select[facs[n/d], Min@@#>=d&]], {d, Rest[Divisors[n]]}]];
stableQ[u_, Q_]:=!Apply[Or, Outer[#1=!=#2&&Q[#1, #2]&, u, u, 1], {0, 1}];
Table[Length[Select[facs[n], stableQ[Union[#], IntegerQ[Log[#1, #2]]&]&]], {n, 100}]
|
|
CROSSREFS
|
Cf. A001055, A001597, A002865, A007916, A052410, A101417, A292886, A303707, A305149, A323053, A323087.
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|