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

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.

Cf. A001222, A046315, A056239, A065516, A084126, A084127, A112798, A128301, A300912, A318990, A320655, A338909, A339362.

Sequence in context: A089169 A291563 A178151 * A050514 A229047 A335841

Adjacent sequences: A087791 A087792 A087793 * A087795 A087796 A087797

Keyword

nonn

Author

Reinhard Zumkeller, Oct 09 2003

Status

approved