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A111059
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Product{k=1 to n} (A005117(k)), the product of the first n squarefree positive integers.
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9
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1, 2, 6, 30, 180, 1260, 12600, 138600, 1801800, 25225200, 378378000, 6432426000, 122216094000, 2566537974000, 56463835428000, 1298668214844000, 33765373585944000, 979195833992376000, 29375875019771280000
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OFFSET
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1,2
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COMMENTS
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Do all terms belong to A242031 (weakly decreasing prime signature)? - Gus Wiseman, May 14 2021
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LINKS
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EXAMPLE
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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.
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)
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MATHEMATICA
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Rest[FoldList[Times, 1, Select[Range[40], SquareFreeQ]]] (* Harvey P. Dale, Jun 14 2011 *)
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PROG
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(PARI) m=30; k=1; for(n=1, m, if(issquarefree(n), print1(k=k*n, ", ")))
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CROSSREFS
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A006881 lists squarefree semiprimes.
A072047 applies Omega to each squarefree number.
A246867 groups squarefree numbers by Heinz weight (row sums: A147655).
A319246 gives the sum of prime indices of each squarefree number.
A329631 lists prime indices of squarefree numbers (reversed: A319247).
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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