A355029 Irregular table read by rows: the n-th row gives the possible values of the number of prime divisors (counted with multiplicity) of numbers with n divisors.

0, 1, 2, 2, 3, 4, 3, 5, 6, 3, 4, 7, 4, 8, 5, 9, 10, 4, 5, 6, 11, 12, 7, 13, 6, 14, 4, 5, 6, 8, 15, 16, 5, 7, 9, 17, 18, 6, 7, 10, 19, 8, 20, 11, 21, 22, 5, 6, 7, 8, 9, 12, 23, 8, 24, 13, 25, 6, 10, 26, 8, 9, 14, 27, 28, 7, 9, 11, 15, 29, 30, 5, 6, 7, 9, 10, 16, 31

Offset: 1

Author

Amiram Eldar, Jun 16 2022

Keywords

• nonn
• tabf

Comments

The n-th row begins with A059975(n) and ends with n-1.

Examples

			Table begins:
  0;
  1;
  2;
  2, 3;
  4;
  3, 5;
  6;
  3, 4, 7;
  4, 8;
  5, 9;
  ...
Numbers k with 4 divisors are either of the form p1 * p2 with p1 and p2 being distinct primes, or of the form p^3 with p prime. The corresponding numbers of prime divisors (counted with multiplicity) are 2 and 3, respectively. Therefore, the 4th row is {2, 3}.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..6758 (rows 1..1000, flattened)

Crossrefs

Cf. A000005, A001222, A059975, A118914, A162247, A355026, A355030 (row lengths).

Programs

Mathematica

Table[Union[Total[#-1]& /@ f[n]], {n, 1, 32}] // Flatten (* using the function f by T. D. Noe at A162247 *)