|
|
A320888
|
|
Number of set multipartitions (multisets of sets) of factorizations of n into factors > 1 such that all the parts have the same product.
|
|
3
|
|
|
1, 1, 1, 2, 1, 2, 1, 3, 2, 2, 1, 3, 1, 2, 2, 4, 1, 3, 1, 3, 2, 2, 1, 5, 2, 2, 3, 3, 1, 5, 1, 4, 2, 2, 2, 8, 1, 2, 2, 5, 1, 5, 1, 3, 3, 2, 1, 7, 2, 3, 2, 3, 1, 5, 2, 5, 2, 2, 1, 9, 1, 2, 3, 9, 2, 5, 1, 3, 2, 5, 1, 9, 1, 2, 3, 3, 2, 5, 1, 7, 4, 2, 1, 9, 2, 2, 2
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,4
|
|
LINKS
|
|
|
FORMULA
|
|
|
EXAMPLE
|
The a(144) = 20 set multipartitions:
(2*3*4*6) (2*8*9) (2*72) (144)
(2*6)*(2*6) (3*6*8) (3*48)
(2*6)*(3*4) (2*3*24) (4*36)
(3*4)*(3*4) (2*4*18) (6*24)
(2*6*12) (8*18)
(3*4*12) (9*16)
(12)*(2*6) (12)*(12)
(12)*(3*4)
|
|
MATHEMATICA
|
strfacs[n_]:=If[n<=1, {{}}, Join@@Table[Map[Prepend[#, d]&, Select[strfacs[n/d], Min@@#>d&]], {d, Rest[Divisors[n]]}]];
Table[With[{g=GCD@@FactorInteger[n][[All, 2]]}, Sum[Binomial[Length[strfacs[n^(1/d)]]+d-1, d], {d, Divisors[g]}]], {n, 100}]
|
|
CROSSREFS
|
Cf. A001055, A001970, A045778, A050336, A052409, A089259, A294786, A296132, A319269, A320886, A320887, A320889.
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|