A339191 Partial products of squarefree semiprimes (A006881).

6, 60, 840, 12600, 264600, 5821200, 151351200, 4994589600, 169816046400, 5943561624000, 225855341712000, 8808358326768000, 405184483031328000, 20664408634597728000, 1136542474902875040000, 64782921069463877280000, 3757409422028904882240000

Offset: 1

Author

Gus Wiseman, Nov 30 2020

Keywords

• nonn

Comments

A squarefree semiprime is a product of any two distinct prime numbers.

Do all terms belong to A242031 (weakly decreasing prime signature)?

Examples

			The sequence of terms together with their prime indices begins:
          6: {1,2}
         60: {1,1,2,3}
        840: {1,1,1,2,3,4}
      12600: {1,1,1,2,2,3,3,4}
     264600: {1,1,1,2,2,2,3,3,4,4}
    5821200: {1,1,1,1,2,2,2,3,3,4,4,5}
  151351200: {1,1,1,1,1,2,2,2,3,3,4,4,5,6}
The sequence of terms together with their prime signatures begins:
                   6: (1,1)
                  60: (2,1,1)
                 840: (3,1,1,1)
               12600: (3,2,2,1)
              264600: (3,3,2,2)
             5821200: (4,3,2,2,1)
           151351200: (5,3,2,2,1,1)
          4994589600: (5,4,2,2,2,1)
        169816046400: (6,4,2,2,2,1,1)
       5943561624000: (6,4,3,3,2,1,1)
     225855341712000: (7,4,3,3,2,1,1,1)
    8808358326768000: (7,5,3,3,2,2,1,1)
  405184483031328000: (8,5,3,3,2,2,1,1,1)
		

Crossrefs

A000040 lists the primes, with partial products A002110 (primorials).

A001358 lists semiprimes, with partial products A112141.

A002100 counts partitions into squarefree semiprimes (restricted: A338903)

A000142 lists factorial numbers, with partial products A000178.

A005117 lists squarefree numbers, with partial products A111059.

A006881 lists squarefree semiprimes, with partial sums A168472.

A166237 gives first differences of squarefree semiprimes.

A320655 counts factorizations into semiprimes.

A320656 counts factorizations into squarefree semiprimes.

A338898/A338912/A338913 give prime indices of semiprimes.

A338899/A270650/A270652 give prime indices of squarefree semiprimes.

A338901 gives first appearances in the list of squarefree semiprimes.

A339113 gives products of primes of squarefree semiprime index.

Cf. A001221, A112798, A167171, A320732, A320891, A320892, A320894, A320911, A338900, A338902, A339003, A339004.

Programs

Mathematica

FoldList[Times,Select[Range[20],SquareFreeQ[#]&&PrimeOmega[#]==2&]]