A367096 Irregular triangle read by rows where row n lists the semiprime divisors of n. Alternatively, row n lists the semiprime divisors of A002808(n).

4, 6, 4, 9, 10, 4, 6, 14, 15, 4, 6, 9, 4, 10, 21, 22, 4, 6, 25, 26, 9, 4, 14, 6, 10, 15, 4, 33, 34, 35, 4, 6, 9, 38, 39, 4, 10, 6, 14, 21, 4, 22, 9, 15, 46, 4, 6, 49, 10, 25, 51, 4, 26, 6, 9, 55, 4, 14, 57, 58, 4, 6, 10, 15, 62, 9, 21, 4, 65, 6, 22, 33, 4, 34

Offset: 1

Author

Gus Wiseman, Nov 08 2023

Keywords

• nonn
• tabf

Comments

On the first interpretation, the first three rows are empty. On the second, the first row is (4).

Examples

			The semiprime divisors of 30 are {6,10,15}, so row 30 is (6,10,15). Without empty rows, this is row 19.
Triangle begins (empty rows indicated by dots):
   1: .
   2: .
   3: .
   4: 4
   5: .
   6: 6
   7: .
   8: 4
   9: 9
  10: 10
  11: .
  12: 4,6
Without empty rows:
   1: 4
   2: 6
   3: 4
   4: 9
   5: 10
   6: 4,6
   7: 14
   8: 15
   9: 4
  10: 6,9
  11: 4,10
  12: 21
		

Crossrefs

For all divisors we have A027750.

Square terms are counted by A056170.

Row sums are A076290.

Squarefree terms are counted by A079275.

Row lengths are A086971, firsts A220264.

A000005 counts divisors.

A001222 counts prime factors (or prime indices), distinct A001221.

A001358 lists semiprimes, squarefree A006881, complement A100959.

Cf. A008967, A365829, A366738, A366739, A366740, A367093, A367098.

Programs

Mathematica

Table[Select[Divisors[n],PrimeOmega[#]==2&],{n,100}]

PARI

row(n) = select(x -> bigomega(x) == 2, divisors(n)); \\ Amiram Eldar, May 02 2025