cp's OEIS Frontend

A339194 Sum of all squarefree semiprimes with greater prime factor prime(n).

%I A339194 #27 Jun 16 2024 05:21:24
%S A339194 0,6,25,70,187,364,697,1102,1771,2900,3999,5920,8077,10234,13207,
%T A339194 17384,22479,26840,33567,40328,46647,56248,65653,77786,93411,107060,
%U A339194 119583,135248,149439,167240,202311,225320,253587,276332,316923,343676,381039,421192,458749
%N A339194 Sum of all squarefree semiprimes with greater prime factor prime(n).
%F A339194 a(n) = prime(n) * Sum_{k=1..n-1} prime(k) = prime(n) * A007504(n-1).
%F A339194 a(n) = A024447(n) - A024447(n-1).
%F A339194 a(n) = A034960(n) - A143215(n). - _Marco Zárate_, Jun 14 2024
%e A339194 The triangle A339116 with row sums equal to this sequence begins (n > 1):
%e A339194     6 = 6
%e A339194    25 = 10 + 15
%e A339194    70 = 14 + 21 + 35
%e A339194   187 = 22 + 33 + 55 + 77
%t A339194 Table[Sum[Prime[i]*Prime[j],{j,i-1}],{i,10}]
%o A339194 (PARI) a(n) = prime(n)*vecsum(primes(n-1)); \\ _Michel Marcus_, Jun 15 2024
%Y A339194 A025129 gives sums of squarefree semiprimes by weight, row sums of A338905.
%Y A339194 A143215 is the not necessarily squarefree version, row sums of A087112.
%Y A339194 A339116 is a triangle of squarefree semiprimes with these row sums.
%Y A339194 A339360 looks at all squarefree numbers, row sums of A339195.
%Y A339194 A001358 lists semiprimes.
%Y A339194 A005117 lists squarefree numbers.
%Y A339194 A006881 lists squarefree semiprimes, with odd terms A046388.
%Y A339194 A024697 is the sum of semiprimes of weight n.
%Y A339194 A168472 gives partial sums of squarefree semiprimes.
%Y A339194 A332765 gives the greatest squarefree semiprime of weight n.
%Y A339194 A338898/A338912/A338913 give the prime indices of semiprimes, with product A087794, sum A176504, and difference A176506.
%Y A339194 A338899/A270650/A270652 give the prime indices of squarefree semiprimes, with difference A338900.
%Y A339194 A338904 groups semiprimes by weight.
%Y A339194 A338907/A338908 list squarefree semiprimes of odd/even weight.
%Y A339194 Cf. A000040, A001221, A014342, A098350, A100484, A319613, A320656, A338901, A339003, A339114/A339115.
%K A339194 nonn
%O A339194 1,2
%A A339194 _Gus Wiseman_, Dec 02 2020