A111059 - OEIS

A111059

Product{k=1 to 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

(list; graph; refs; listen; history; text; internal format)

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

AUTHOR

Leroy Quet, Oct 07 2005

EXTENSIONS

More terms from Klaus Brockhaus, Oct 08 2005

STATUS

approved