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

1,1

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.

Links

Table of n, a(n) for n=1..69.

Formula

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

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

Example

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

Mathematica

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

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.

Sequence in context: A119476 A358700 A307136 * A240676 A037038 A348133

Adjacent sequences: A339359 A339360 A339361 * A339363 A339364 A339365

Keyword

nonn

Author

Gus Wiseman, Dec 06 2020

Status

approved