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%I #20 May 14 2021 22:39:02
%S 1,2,6,30,180,1260,12600,138600,1801800,25225200,378378000,6432426000,
%T 122216094000,2566537974000,56463835428000,1298668214844000,
%U 33765373585944000,979195833992376000,29375875019771280000
%N Product{k=1 to n} (A005117(k)), the product of the first n squarefree positive integers.
%C Do all terms belong to A242031 (weakly decreasing prime signature)? - _Gus Wiseman_, May 14 2021
%H Charles R Greathouse IV, <a href="/A111059/b111059.txt">Table of n, a(n) for n = 1..417</a>
%e 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.
%e From _Gus Wiseman_, May 14 2021: (Start)
%e The sequence of terms together with their prime signatures begins:
%e 1: ()
%e 2: (1)
%e 6: (1,1)
%e 30: (1,1,1)
%e 180: (2,2,1)
%e 1260: (2,2,1,1)
%e 12600: (3,2,2,1)
%e 138600: (3,2,2,1,1)
%e 1801800: (3,2,2,1,1,1)
%e 25225200: (4,2,2,2,1,1)
%e 378378000: (4,3,3,2,1,1)
%e 6432426000: (4,3,3,2,1,1,1)
%e 122216094000: (4,3,3,2,1,1,1,1)
%e (End)
%t Rest[FoldList[Times,1,Select[Range[40],SquareFreeQ]]] (* _Harvey P. Dale_, Jun 14 2011 *)
%o (PARI) m=30;k=1;for(n=1,m,if(issquarefree(n),print1(k=k*n,",")))
%Y A005117 lists squarefree numbers.
%Y A006881 lists squarefree semiprimes.
%Y A072047 applies Omega to each squarefree number.
%Y A246867 groups squarefree numbers by Heinz weight (row sums: A147655).
%Y A261144 groups squarefree numbers by smoothness (row sums: A054640).
%Y A319246 gives the sum of prime indices of each squarefree number.
%Y A329631 lists prime indices of squarefree numbers (reversed: A319247).
%Y Cf. A001221, A002110, A014466, A070826, A338901, A339360.
%K nonn
%O 1,2
%A _Leroy Quet_, Oct 07 2005
%E More terms from _Klaus Brockhaus_, Oct 08 2005
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