A338904 Irregular triangle read by rows where row n lists all semiprimes whose prime indices sum to n.

4, 6, 9, 10, 14, 15, 21, 22, 25, 26, 33, 35, 34, 39, 49, 55, 38, 51, 65, 77, 46, 57, 85, 91, 121, 58, 69, 95, 119, 143, 62, 87, 115, 133, 169, 187, 74, 93, 145, 161, 209, 221, 82, 111, 155, 203, 247, 253, 289, 86, 123, 185, 217, 299, 319, 323, 94, 129, 205

Offset: 2

Author

Gus Wiseman, Nov 28 2020

Keywords

• nonn
• tabf

Comments

A semiprime is a product of any two 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:
   4
   6
   9  10
  14  15
  21  22  25
  26  33  35
  34  39  49  55
  38  51  65  77
  46  57  85  91 121
  58  69  95 119 143
  62  87 115 133 169 187
  74  93 145 161 209 221
  82 111 155 203 247 253 289
  86 123 185 217 299 319 323
  94 129 205 259 341 361 377 391
		

Crossrefs

A004526 gives row lengths.

A024697 gives row sums.

A087112 is a different triangle of semiprimes.

A098350 has antidiagonals with the same distinct terms as these rows.

A338905 is the squarefree case, with row sums A025129.

A338907/A338906 are the union of odd/even rows.

A339114/A339115 are the row minima/maxima.

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

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

A014342 is the self-convolution of primes.

A037143 lists primes and semiprimes.

A056239 gives sum of prime indices (Heinz weight).

A062198 gives partial sums of semiprimes.

A084126 and A084127 give the prime factors of semiprimes.

A289182/A115392 list the positions of odd/even terms in A001358.

A332765 gives the greatest squarefree semiprime of weight n.

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, A001222, A005117, A112798, A320732, A332877, A338908, A338910, A338911, A339116.

Programs

Mathematica

Table[Sort[Table[Prime[k]*Prime[n-k],{k,n/2}]],{n,2,10}]