OFFSET
1,210
COMMENTS
A squarefree semiprime (A006881) is a product of any two distinct prime numbers.
Also the number of strict multiset partitions of the multiset of prime factors of n, into distinct strict pairs.
LINKS
EXAMPLE
The a(n) factorizations for n = 210, 1260, 4620, 30030, 69300 are respectively 3, 2, 6, 15, 7:
(6*35) (6*10*21) (6*10*77) (6*55*91) (6*10*15*77)
(10*21) (6*14*15) (6*14*55) (6*65*77) (6*10*21*55)
(14*15) (6*22*35) (10*33*91) (6*10*33*35)
(10*14*33) (10*39*77) (6*14*15*55)
(10*21*22) (14*33*65) (6*15*22*35)
(14*15*22) (14*39*55) (10*14*15*33)
(15*22*91) (10*15*21*22)
(15*26*77)
(21*22*65)
(21*26*55)
(22*35*39)
(26*33*35)
(6*35*143)
(10*21*143)
(14*15*143)
MATHEMATICA
bfacs[n_]:=If[n<=1, {{}}, Join@@Table[Map[Prepend[#, d]&, Select[bfacs[n/d], Min@@#>d&]], {d, Select[Rest[Divisors[n]], SquareFreeQ[#]&&PrimeOmega[#]==2&]}]];
Table[Length[bfacs[n]], {n, 100}]
PROG
CROSSREFS
A320656 is the not necessarily strict version.
A320911 lists all (not just distinct) products of squarefree semiprimes.
A322794 counts uniform factorizations, such as these.
A339561 lists positions of nonzero terms.
The following count vertex-degree partitions and give their Heinz numbers:
The following count partitions of even length and give their Heinz numbers:
KEYWORD
nonn
AUTHOR
Gus Wiseman, Dec 19 2020
EXTENSIONS
More terms and secondary offset added by Antti Karttunen, May 02 2022
STATUS
approved