The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A339887 Number of factorizations of n into primes or squarefree semiprimes. 4
 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 2, 1, 1, 2, 1, 2, 2, 2, 1, 2, 1, 2, 1, 2, 1, 4, 1, 1, 2, 2, 2, 3, 1, 2, 2, 2, 1, 4, 1, 2, 2, 2, 1, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 5, 1, 2, 2, 1, 2, 4, 1, 2, 2, 4, 1, 3, 1, 2, 2, 2, 2, 4, 1, 2, 1, 2, 1, 5, 2, 2, 2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,6 COMMENTS A squarefree semiprime (A006881) is a product of any two distinct prime numbers. Conjecture: also the number of semistandard Young tableaux whose entries are the prime indices of n (A323437). Is this a duplicate of A323437? - R. J. Mathar, Jan 05 2021 LINKS FORMULA a(A002110(n)) = A000085(n), and in general if n is a product of k distinct primes, a(n) = A000085(k). a(n) = Sum_{d|n} A320656(n/d), so A320656 is the Moebius transform of this sequence. EXAMPLE The a(n) factorizations for n = 36, 60, 180, 360, 420, 840:   6*6       6*10      5*6*6       6*6*10        2*6*35      6*10*14   2*3*6     2*5*6     2*6*15      2*5*6*6       5*6*14      2*2*6*35   2*2*3*3   2*2*15    3*6*10      2*2*6*15      6*7*10      2*5*6*14             2*3*10    2*3*5*6     2*3*6*10      2*10*21     2*6*7*10             2*2*3*5   2*2*3*15    2*2*3*5*6     2*14*15     2*2*10*21                       2*3*3*10    2*2*2*3*15    2*5*6*7     2*2*14*15                       2*2*3*3*5   2*2*3*3*10    3*10*14     2*2*5*6*7                                   2*2*2*3*3*5   2*2*3*35    2*3*10*14                                                 2*2*5*21    2*2*2*3*35                                                 2*2*7*15    2*2*2*5*21                                                 2*3*5*14    2*2*2*7*15                                                 2*3*7*10    2*2*3*5*14                                                 2*2*3*5*7   2*2*3*7*10                                                             2*2*2*3*5*7 MATHEMATICA sqpe[n_]:=If[n<=1, {{}}, Join@@Table[Map[Prepend[#, d]&, Select[sqpe[n/d], Min@@#>=d&]], {d, Select[Divisors[n], PrimeQ[#]||SquareFreeQ[#]&&PrimeOmega[#]==2&]}]]; Table[Length[sqpe[n]], {n, 100}] CROSSREFS See link for additional cross-references. Only allowing only primes gives A008966. Not allowing primes gives A320656. Unlabeled multiset partitions of this type are counted by A320663/A339888. Allowing squares of primes gives A320732. The strict version is A339742. A001055 counts factorizations. A001358 lists semiprimes, with squarefree case A006881. A002100 counts partitions into squarefree semiprimes. A338899/A270650/A270652 give the prime indices of squarefree semiprimes. Cf. A000070, A000961, A001221, A096373, A320893, A338914, A339740, A339741, A339841, A339846. Sequence in context: A318369 A007875 A323437 * A259936 A050320 A333175 Adjacent sequences:  A339884 A339885 A339886 * A339888 A339889 A339890 KEYWORD nonn AUTHOR Gus Wiseman, Dec 22 2020 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified August 1 00:13 EDT 2021. Contains 346377 sequences. (Running on oeis4.)