OFFSET
1,16
EXAMPLE
The a(n) factorizations for n = 16, 64, 72, 144, 192, 256, 288:
(16) (64) (72) (144) (192) (256) (288)
(4*4) (8*8) (8*9) (4*36) (4*48) (4*64) (4*72)
(4*16) (4*18) (8*18) (8*24) (8*32) (8*36)
(4*4*4) (9*16) (12*16) (16*16) (9*32)
(12*12) (4*4*12) (4*8*8) (12*24)
(4*4*9) (4*4*16) (16*18)
(4*4*4*4) (4*8*9)
(4*4*18)
MATHEMATICA
facs[n_]:=If[n<=1, {{}}, Join@@Table[Map[Prepend[#, d]&, Select[facs[n/d], Min@@#>=d&]], {d, Rest[Divisors[n]]}]];
Table[Length[Select[facs[n], NoneTrue[SquareFreeQ]]], {n, 100}]
CROSSREFS
For prime-powers we have A000688.
For nonprime numbers we have A050370.
The version for partitions is A114374.
For perfect-powers we have A294068.
For non-perfect-powers we have A303707.
For non-prime-powers we have A322452.
The strict case is A376679.
Nonsquarefree numbers:
- A078147 (first differences)
- A376593 (second differences)
- A376594 (inflections and undulations)
- A376595 (nonzero curvature)
KEYWORD
nonn
AUTHOR
Gus Wiseman, Oct 07 2024
STATUS
approved