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

1,1

Comments

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

Links

Table of n, a(n) for n=1..74.

Example

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

Mathematica

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

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.

Sequence in context: A010300 A113209 A367731 * A088739 A088740 A088738

Adjacent sequences: A367093 A367094 A367095 * A367097 A367098 A367099

Keyword

nonn,tabf

Author

Gus Wiseman, Nov 08 2023

Status

approved