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

1,2

Links

Table of n, a(n) for n=1..39.

Formula

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

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

Example

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

Mathematica

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

Prog

(PARI) a(n) = prime(n)*sum(k=1, n-1, prime(k)); \\ Michel Marcus, Dec 04 2020

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.

Sequence in context: A245679 A354392 A211911 * A241303 A278473 A281157

Adjacent sequences: A339191 A339192 A339193 * A339195 A339196 A339197

Keyword

nonn

Author

Gus Wiseman, Dec 02 2020

Status

approved