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

1,2

Comments

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

Links

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

Example

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)

Mathematica

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

Prog

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

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.

Sequence in context: A353184 A096769 A365975 * A009645 A274966 A293653

Adjacent sequences: A111056 A111057 A111058 * A111060 A111061 A111062

Keyword

nonn,changed

Author

Leroy Quet, Oct 07 2005

Extensions

More terms from Klaus Brockhaus, Oct 08 2005

Status

approved