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

0, 6, 25, 70, 187, 364, 697, 1102, 1771, 2900, 3999, 5920, 8077, 10234, 13207, 17384, 22479, 26840, 33567, 40328, 46647, 56248, 65653, 77786, 93411, 107060, 119583, 135248, 149439, 167240, 202311, 225320, 253587, 276332, 316923, 343676, 381039, 421192, 458749

Offset: 1

Author

Gus Wiseman, Dec 02 2020

Keywords

• nonn

Examples

			The triangle A339116 with row sums equal to this sequence begins (n > 1):
    6 = 6
   25 = 10 + 15
   70 = 14 + 21 + 35
  187 = 22 + 33 + 55 + 77
		

Crossrefs

A025129 gives sums of squarefree semiprimes by weight, row sums of A338905.

A143215 is the not necessarily squarefree version, row sums of A087112.

A339116 is a triangle of squarefree semiprimes with these row sums.

A339360 looks at all squarefree numbers, row sums of A339195.

A001358 lists semiprimes.

A005117 lists squarefree numbers.

A006881 lists squarefree semiprimes, with odd terms A046388.

A024697 is the sum of semiprimes of weight n.

A168472 gives partial sums of squarefree semiprimes.

A332765 gives the greatest squarefree semiprime of weight n.

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

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

A338904 groups semiprimes by weight.

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

Cf. A000040, A001221, A014342, A098350, A100484, A319613, A320656, A338901, A339003, A339114/A339115.

Programs

Mathematica

Table[Sum[Prime[i]*Prime[j],{j,i-1}],{i,10}]

PARI

a(n) = prime(n)*vecsum(primes(n-1)); \\ Michel Marcus, Jun 15 2024

Formula

a(n) = prime(n) * Sum_{k=1..n-1} prime(k) = prime(n) * A007504(n-1).

a(n) = A024447(n) - A024447(n-1).

a(n) = A034960(n) - A143215(n). - Marco Zárate, Jun 14 2024