A339362 - OEIS

%I #6 Dec 07 2020 01:52:11

%S 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,

%T 16,11,17,14,12,18,11,19,15,16,12,20,17,21,11,13,22,14,23,18,13,24,19,

%U 25,20,15,12,26,21,27,14,16,28,13,22,29,17,15,30,23,13

%N Sum of prime indices of the n-th squarefree semiprime.

%C 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.

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

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

%e The sequence of all squarefree semiprimes together with the sums of their prime indices begins:

%e    6: 1 + 2 = 3

%e   10: 1 + 3 = 4

%e   14: 1 + 4 = 5

%e   15: 2 + 3 = 5

%e   21: 2 + 4 = 6

%e   22: 1 + 5 = 6

%e   26: 1 + 6 = 7

%e   33: 2 + 5 = 7

%e   34: 1 + 7 = 8

%e   35: 3 + 4 = 7

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

%Y A001358 lists semiprimes.

%Y A003963 gives the product of prime indices of n.

%Y A005117 lists squarefree numbers.

%Y A006881 lists squarefree semiprimes.

%Y A025129 gives the sum of squarefree semiprimes of weight n.

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

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

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

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

%Y A338904 groups semiprimes by weight.

%Y A338905 groups squarefree semiprimes by weight.

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

%Y A339116 groups squarefree semiprimes by greater prime factor.

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

%K nonn

%O 1,1

%A _Gus Wiseman_, Dec 06 2020