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

%I A111059 #22 Jan 08 2025 15:16:00
%S A111059 1,2,6,30,180,1260,12600,138600,1801800,25225200,378378000,6432426000,
%T A111059 122216094000,2566537974000,56463835428000,1298668214844000,
%U A111059 33765373585944000,979195833992376000,29375875019771280000
%N A111059 a(n) = Product_{k=1..n} A005117(k), the product of the first n squarefree positive integers.
%C A111059 Do all terms belong to A242031 (weakly decreasing prime signature)? - _Gus Wiseman_, May 14 2021
%H A111059 Charles R Greathouse IV, <a href="/A111059/b111059.txt">Table of n, a(n) for n = 1..417</a>
%e A111059 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 A111059 From _Gus Wiseman_, May 14 2021: (Start)
%e A111059 The sequence of terms together with their prime signatures begins:
%e A111059              1: ()
%e A111059              2: (1)
%e A111059              6: (1,1)
%e A111059             30: (1,1,1)
%e A111059            180: (2,2,1)
%e A111059           1260: (2,2,1,1)
%e A111059          12600: (3,2,2,1)
%e A111059         138600: (3,2,2,1,1)
%e A111059        1801800: (3,2,2,1,1,1)
%e A111059       25225200: (4,2,2,2,1,1)
%e A111059      378378000: (4,3,3,2,1,1)
%e A111059     6432426000: (4,3,3,2,1,1,1)
%e A111059   122216094000: (4,3,3,2,1,1,1,1)
%e A111059 (End)
%t A111059 Rest[FoldList[Times,1,Select[Range[40],SquareFreeQ]]] (* _Harvey P. Dale_, Jun 14 2011 *)
%o A111059 (PARI) m=30;k=1;for(n=1,m,if(issquarefree(n),print1(k=k*n,",")))
%Y A111059 A005117 lists squarefree numbers.
%Y A111059 A006881 lists squarefree semiprimes.
%Y A111059 A072047 applies Omega to each squarefree number.
%Y A111059 A246867 groups squarefree numbers by Heinz weight (row sums: A147655).
%Y A111059 A261144 groups squarefree numbers by smoothness (row sums: A054640).
%Y A111059 A319246 gives the sum of prime indices of each squarefree number.
%Y A111059 A329631 lists prime indices of squarefree numbers (reversed: A319247).
%Y A111059 Cf. A001221, A002110, A014466, A070826, A338901, A339360.
%K A111059 nonn
%O A111059 1,2
%A A111059 _Leroy Quet_, Oct 07 2005
%E A111059 More terms from _Klaus Brockhaus_, Oct 08 2005