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%I #9 Dec 18 2020 07:56:28
%S 1,2,4,3,4,6,8,5,9,6,10,7,12,8,12,9,16,14,15,16,10,11,18,18,12,20,13,
%T 21,14,20,24,22,15,24,16,24,27,17,28,25,18,26,28,32,19,30,20,30,30,21,
%U 33,22,32,36,23,36,34,24,36,36,35,25,38,26,40,39,27,40,40,28,42,44,29
%N Products of prime-indices of factors of semiprimes.
%C A semiprime (A001358) is a product of any two 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. - _Gus Wiseman_, Dec 04 2020
%F a(n) = A049084(A084126(n))*A049084(A084127(n)) = A003963(A001358(n)).
%F a(n) = A003963(A001358(n)) = A338912(n) * A338913(n). - _Gus Wiseman_, Dec 04 2020
%e A001358(20)=57=3*19=A000040(2)*A000040(8), therefore a(20)=2*8=16.
%e From _Gus Wiseman_, Dec 04 2020: (Start)
%e The sequence of all semiprimes together with the products of their prime indices begins:
%e 4: 1 * 1 = 1
%e 6: 1 * 2 = 2
%e 9: 2 * 2 = 4
%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 25: 3 * 3 = 9
%e 26: 1 * 6 = 6
%e (End)
%t Table[If[SquareFreeQ[n],Times@@PrimePi/@First/@FactorInteger[n],PrimePi[Sqrt[n]]^2],{n,Select[Range[100],PrimeOmega[#]==2&]}] (* _Gus Wiseman_, Dec 04 2020 *)
%Y A003963 is the version for not just semiprimes.
%Y A176504 gives the sum of the same two indices.
%Y A176506 gives the difference of the same two indices.
%Y A339361 is the squarefree case.
%Y A001358 lists semiprimes.
%Y A006881 lists squarefree semiprimes.
%Y A289182/A115392 list the positions of odd/even terms of A001358.
%Y A338898/A338912/A338913 give the prime indices of semiprimes.
%Y A338899/A270650/A270652 give the prime indices of squarefree semiprimes.
%Y A338904 groups semiprimes by weight.
%Y Cf. A001222, A046315, A056239, A065516, A084126, A084127, A112798, A128301, A300912, A318990, A320655, A338909, A339362.
%K nonn
%O 1,2
%A _Reinhard Zumkeller_, Oct 09 2003
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