A339362 Sum of prime indices of the n-th squarefree semiprime.

3, 4, 5, 5, 6, 6, 7, 7, 8, 7, 9, 8, 10, 9, 8, 10, 11, 12, 9, 11, 13, 9, 14, 10, 15, 12, 10, 13, 16, 11, 17, 14, 12, 18, 11, 19, 15, 16, 12, 20, 17, 21, 11, 13, 22, 14, 23, 18, 13, 24, 19, 25, 20, 15, 12, 26, 21, 27, 14, 16, 28, 13, 22, 29, 17, 15, 30, 23, 13

Offset: 1

Author

Gus Wiseman, Dec 06 2020

Keywords

• nonn

Comments

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.

Examples

			The sequence of all squarefree semiprimes together with the sums of their prime indices begins:
   6: 1 + 2 = 3
  10: 1 + 3 = 4
  14: 1 + 4 = 5
  15: 2 + 3 = 5
  21: 2 + 4 = 6
  22: 1 + 5 = 6
  26: 1 + 6 = 7
  33: 2 + 5 = 7
  34: 1 + 7 = 8
  35: 3 + 4 = 7
		

Crossrefs

A001358 lists semiprimes.

A003963 gives the product of prime indices of n.

A005117 lists squarefree numbers.

A006881 lists squarefree semiprimes.

A025129 gives the sum of squarefree semiprimes of weight n.

A056239 (weight) gives the sum of prime indices of n.

A332765/A339114 give the greatest/least squarefree semiprime of weight n.

A338898/A338912/A338913 give the prime indices of semiprimes, with product/sum/difference A087794/A176504/A176506.

A338899/A270650/A270652 give the prime indices of squarefree semiprimes, with product/sum/difference A339361/A339362/A338900.

A338904 groups semiprimes by weight.

A338905 groups squarefree semiprimes by weight.

A338907/A338908 list squarefree semiprimes of odd/even weight.

A339116 groups squarefree semiprimes by greater prime factor.

Cf. A001221, A046388, A065516, A112798, A115392, A166237, A320656, A338901, A339003, A339004.

Programs

Mathematica

Table[Plus@@PrimePi/@First/@FactorInteger[n],{n,Select[Range[100],SquareFreeQ[#]&&PrimeOmega[#]==2&]}]

Formula

a(n) = A056239(A006881(n)).

a(n) = A270650(n) + A270652(n).