A339116 Triangle of all squarefree semiprimes grouped by greater prime factor, read by rows.

6, 10, 15, 14, 21, 35, 22, 33, 55, 77, 26, 39, 65, 91, 143, 34, 51, 85, 119, 187, 221, 38, 57, 95, 133, 209, 247, 323, 46, 69, 115, 161, 253, 299, 391, 437, 58, 87, 145, 203, 319, 377, 493, 551, 667, 62, 93, 155, 217, 341, 403, 527, 589, 713, 899

Offset: 2

Author

Gus Wiseman, Dec 01 2020

Keywords

• nonn
• easy
• tabl

Comments

A squarefree semiprime is a product of any two distinct prime numbers.

Examples

			Triangle begins:
   6
  10  15
  14  21  35
  22  33  55  77
  26  39  65  91 143
  34  51  85 119 187 221
  38  57  95 133 209 247 323
  46  69 115 161 253 299 391 437
  58  87 145 203 319 377 493 551 667
  62  93 155 217 341 403 527 589 713 899
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 2..1276 (first 50 rows)

Crossrefs

A339194 gives row sums.

A100484 is column k = 1.

A001748 is column k = 2.

A001750 is column k = 3.

A006094 is column k = n - 1.

A090076 is column k = n - 2.

A319613 is the central column k = 2*n.

A087112 is the not necessarily squarefree version.

A338905 is a different triangle of squarefree semiprimes.

A339195 is the generalization to all squarefree numbers, row sums A339360.

A001358 lists semiprimes.

A005117 lists squarefree numbers.

A006881 lists squarefree semiprimes, with odd terms A046388.

A024697 is the sum of semiprimes of weight n.

A025129 is the sum of squarefree semiprimes of weight n.

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, A112798, A168472, A320656, A338901, A339003, A339114/A339115.

Subsequence of A019565.

Programs

Mathematica

Table[Prime[i]*Prime[j],{i,2,10},{j,i-1}]

PARI

row(n) = {prime(n)*primes(n-1)}
{ for(n=2, 10, print(row(n))) } \\ Andrew Howroyd, Jan 19 2023

Formula

T(n,k) = prime(n) * prime(k) for k < n.

Extensions

Offset corrected by Andrew Howroyd, Jan 19 2023