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%I #9 Dec 07 2020 01:52:00
%S 2,3,4,6,8,5,6,10,7,12,8,12,9,14,15,16,10,11,18,18,12,20,13,21,14,20,
%T 24,22,15,24,16,24,27,17,28,18,26,28,32,19,30,20,30,30,21,33,22,32,36,
%U 23,34,24,36,36,35,25,38,26,40,39,27,40,40,28,42,44,29,42
%N Product of prime indices of the n-th squarefree semiprime.
%C A squarefree semiprime (A006881) is a product of any two distinct prime numbers. A prime index of n is a number m such that the m-th prime number divides n. The multiset of prime indices of n is row n of A112798.
%F a(n) = A003963(A006881(n)).
%F a(n) = A270650(n) * A270652(n).
%e The sequence of all squarefree semiprimes together with the products of their prime indices begins:
%e 6: 1 * 2 = 2
%e 10: 1 * 3 = 3
%e 14: 1 * 4 = 4
%e 15: 2 * 3 = 6
%e 21: 2 * 4 = 8
%e 22: 1 * 5 = 5
%e 26: 1 * 6 = 6
%e 33: 2 * 5 = 10
%e 34: 1 * 7 = 7
%e 35: 3 * 4 = 12
%t Table[Times@@PrimePi/@First/@FactorInteger[n],{n,Select[Range[100],SquareFreeQ[#]&&PrimeOmega[#]==2&]}]
%Y A001358 lists semiprimes.
%Y A003963 gives the product of prime indices of n.
%Y A005117 lists squarefree numbers.
%Y A006881 lists squarefree semiprimes.
%Y A025129 is the sum of squarefree semiprimes of weight n.
%Y A332765/A339114 give the greatest/least squarefree semiprime of weight n.
%Y A338898/A338912/A338913 give the prime indices of semiprimes, with product/sum/difference A087794/A176504/A176506.
%Y A338899/A270650/A270652 give the prime indices of squarefree semiprimes, with product/sum/difference A339361/A339362/A338900.
%Y A338905 groups squarefree semiprimes by weight.
%Y A338907/A338908 list squarefree semiprimes of odd/even weight.
%Y A339116 groups squarefree semiprimes by greater prime factor.
%Y Cf. A001221, A046388, A056239 (weight), A112798, A166237, A320656, A320911, A338901, A339002, A339003, A339004.
%K nonn
%O 1,1
%A _Gus Wiseman_, Dec 06 2020
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