A087794 - OEIS

A087794

Products of prime-indices of factors of semiprimes.

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, 21, 14, 20, 24, 22, 15, 24, 16, 24, 27, 17, 28, 25, 18, 26, 28, 32, 19, 30, 20, 30, 30, 21, 33, 22, 32, 36, 23, 36, 34, 24, 36, 36, 35, 25, 38, 26, 40, 39, 27, 40, 40, 28, 42, 44, 29

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OFFSET

1,2

COMMENTS

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

LINKS

Table of n, a(n) for n=1..73.

FORMULA

a(n) = A049084(A084126(n))*A049084(A084127(n)) = A003963(A001358(n)).

a(n) = A003963(A001358(n)) = A338912(n) * A338913(n). - Gus Wiseman, Dec 04 2020

EXAMPLE

A001358(20)=57=3*19=A000040(2)*A000040(8), therefore a(20)=2*8=16.

From Gus Wiseman, Dec 04 2020: (Start)

The sequence of all semiprimes together with the products of their prime indices begins:

4: 1 * 1 = 1

6: 1 * 2 = 2

9: 2 * 2 = 4

10: 1 * 3 = 3

14: 1 * 4 = 4

15: 2 * 3 = 6

21: 2 * 4 = 8

22: 1 * 5 = 5

25: 3 * 3 = 9

26: 1 * 6 = 6

(End)

MATHEMATICA

Table[If[SquareFreeQ[n], Times@@PrimePi/@First/@FactorInteger[n], PrimePi[Sqrt[n]]^2], {n, Select[Range[100], PrimeOmega[#]==2&]}] (* Gus Wiseman, Dec 04 2020 *)

CROSSREFS

A003963 is the version for not just semiprimes.

A176504 gives the sum of the same two indices.

A176506 gives the difference of the same two indices.

A339361 is the squarefree case.

A001358 lists semiprimes.

A006881 lists squarefree semiprimes.

A289182/A115392 list the positions of odd/even terms of A001358.

A338898/A338912/A338913 give the prime indices of semiprimes.

A338899/A270650/A270652 give the prime indices of squarefree semiprimes.

A338904 groups semiprimes by weight.