cp's OEIS Frontend

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

%I A339362 #6 Dec 07 2020 01:52:11
%S A339362 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 A339362 16,11,17,14,12,18,11,19,15,16,12,20,17,21,11,13,22,14,23,18,13,24,19,
%U A339362 25,20,15,12,26,21,27,14,16,28,13,22,29,17,15,30,23,13
%N A339362 Sum of prime indices of the n-th squarefree semiprime.
%C A339362 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 A339362 a(n) = A056239(A006881(n)).
%F A339362 a(n) = A270650(n) + A270652(n).
%e A339362 The sequence of all squarefree semiprimes together with the sums of their prime indices begins:
%e A339362    6: 1 + 2 = 3
%e A339362   10: 1 + 3 = 4
%e A339362   14: 1 + 4 = 5
%e A339362   15: 2 + 3 = 5
%e A339362   21: 2 + 4 = 6
%e A339362   22: 1 + 5 = 6
%e A339362   26: 1 + 6 = 7
%e A339362   33: 2 + 5 = 7
%e A339362   34: 1 + 7 = 8
%e A339362   35: 3 + 4 = 7
%t A339362 Table[Plus@@PrimePi/@First/@FactorInteger[n],{n,Select[Range[100],SquareFreeQ[#]&&PrimeOmega[#]==2&]}]
%Y A339362 A001358 lists semiprimes.
%Y A339362 A003963 gives the product of prime indices of n.
%Y A339362 A005117 lists squarefree numbers.
%Y A339362 A006881 lists squarefree semiprimes.
%Y A339362 A025129 gives the sum of squarefree semiprimes of weight n.
%Y A339362 A056239 (weight) gives the sum of prime indices of n.
%Y A339362 A332765/A339114 give the greatest/least squarefree semiprime of weight n.
%Y A339362 A338898/A338912/A338913 give the prime indices of semiprimes, with product/sum/difference A087794/A176504/A176506.
%Y A339362 A338899/A270650/A270652 give the prime indices of squarefree semiprimes, with product/sum/difference A339361/A339362/A338900.
%Y A339362 A338904 groups semiprimes by weight.
%Y A339362 A338905 groups squarefree semiprimes by weight.
%Y A339362 A338907/A338908 list squarefree semiprimes of odd/even weight.
%Y A339362 A339116 groups squarefree semiprimes by greater prime factor.
%Y A339362 Cf. A001221, A046388, A065516, A112798, A115392, A166237, A320656, A338901, A339003, A339004.
%K A339362 nonn
%O A339362 1,1
%A A339362 _Gus Wiseman_, Dec 06 2020