A338905 Irregular triangle read by rows where row n lists all squarefree semiprimes with prime indices summing to n.

6, 10, 14, 15, 21, 22, 26, 33, 35, 34, 39, 55, 38, 51, 65, 77, 46, 57, 85, 91, 58, 69, 95, 119, 143, 62, 87, 115, 133, 187, 74, 93, 145, 161, 209, 221, 82, 111, 155, 203, 247, 253, 86, 123, 185, 217, 299, 319, 323, 94, 129, 205, 259, 341, 377, 391, 106, 141

Offset: 3

Author

Gus Wiseman, Nov 28 2020

Keywords

• nonn
• tabf

Comments

A squarefree semiprime 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.

Examples

			Triangle begins:
   6
  10
  14  15
  21  22
  26  33  35
  34  39  55
  38  51  65  77
  46  57  85  91
  58  69  95 119 143
  62  87 115 133 187
  74  93 145 161 209 221
  82 111 155 203 247 253
  86 123 185 217 299 319 323
		

Crossrefs

A004526 (shifted right) gives row lengths.

A025129 (shifted right) gives row sums.

A056239 gives sum of prime indices (Heinz weight).

A339116 is a different triangle whose diagonals are these rows.

A338904 is the not necessarily squarefree version, with row sums A024697.

A338907/A338908 are the union of odd/even rows.

A339114/A332765 are the row minima/maxima.

A001358 lists semiprimes, with odd/even terms A046315/A100484.

A005117 lists squarefree numbers.

A006881 lists squarefree semiprimes, with odd/even terms A046388/A100484.

A087112 groups semiprimes by greater factor.

A168472 gives partial sums of squarefree semiprimes.

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

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

Cf. A000040, A001221, A014342, A098350, A112798, A320656, A338901, A338906, A339003, A339004, A339005, A339115.

Programs

Mathematica

Table[Sort[Table[Prime[k]*Prime[n-k],{k,(n-1)/2}]],{n,3,10}]