A111059 a(n) = Product_{k=1..n} A005117(k), the product of the first n squarefree positive integers.

1, 2, 6, 30, 180, 1260, 12600, 138600, 1801800, 25225200, 378378000, 6432426000, 122216094000, 2566537974000, 56463835428000, 1298668214844000, 33765373585944000, 979195833992376000, 29375875019771280000

Offset: 1

Author

Leroy Quet, Oct 07 2005

Keywords

• nonn

Comments

Do all terms belong to A242031 (weakly decreasing prime signature)? - Gus Wiseman, May 14 2021

Examples

			Since the first 6 squarefree positive integers are 1, 2, 3, 5, 6, 7, the 6th term of the sequence is 1*2*3*5*6*7 = 1260.
From _Gus Wiseman_, May 14 2021: (Start)
The sequence of terms together with their prime signatures begins:
             1: ()
             2: (1)
             6: (1,1)
            30: (1,1,1)
           180: (2,2,1)
          1260: (2,2,1,1)
         12600: (3,2,2,1)
        138600: (3,2,2,1,1)
       1801800: (3,2,2,1,1,1)
      25225200: (4,2,2,2,1,1)
     378378000: (4,3,3,2,1,1)
    6432426000: (4,3,3,2,1,1,1)
  122216094000: (4,3,3,2,1,1,1,1)
(End)
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..417

Crossrefs

A005117 lists squarefree numbers.

A006881 lists squarefree semiprimes.

A072047 applies Omega to each squarefree number.

A246867 groups squarefree numbers by Heinz weight (row sums: A147655).

A261144 groups squarefree numbers by smoothness (row sums: A054640).

A319246 gives the sum of prime indices of each squarefree number.

A329631 lists prime indices of squarefree numbers (reversed: A319247).

Cf. A001221, A002110, A014466, A070826, A338901, A339360.

Programs

Mathematica

Rest[FoldList[Times,1,Select[Range[40],SquareFreeQ]]] (* Harvey P. Dale, Jun 14 2011 *)

PARI

m=30;k=1;for(n=1,m,if(issquarefree(n),print1(k=k*n,",")))

Extensions

More terms from Klaus Brockhaus, Oct 08 2005