A323305 Number of divisors of the number of prime factors of n counted with multiplicity.

1, 1, 1, 2, 1, 2, 1, 2, 2, 2, 1, 2, 1, 2, 2, 3, 1, 2, 1, 2, 2, 2, 1, 3, 2, 2, 2, 2, 1, 2, 1, 2, 2, 2, 2, 3, 1, 2, 2, 3, 1, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 3, 2, 3, 2, 2, 1, 3, 1, 2, 2, 4, 2, 2, 1, 2, 2, 2, 1, 2, 1, 2, 2, 2, 2, 2, 1, 2, 3, 2, 1, 3, 2, 2, 2

Offset

1,4

Comments

a(1) = 1 by convention.

First differs from A036430 at a(64) = 4, A036430(64) = 3.

Links

Table of n, a(n) for n=1..87.

Formula

a(n) = A000005(A001222(n)).

Mathematica

Array[Length@*Divisors@*PrimeOmega, 100]

Prog

(PARI) a(n) = if (n==1, 1, numdiv(bigomega(n))); \\ Michel Marcus, Jan 13 2019

Crossrefs

Positions of 1's are 1 and the prime numbers A008578.

Positions of 2's are A063989.

Cf. A000005, A001222, A067028, A167175, A323295, A323350.

Sequence in context: A024935 A082477 A036430 * A322794 A163377 A290085

Adjacent sequences: A323302 A323303 A323304 * A323306 A323307 A323308

Keyword

nonn

Author

Gus Wiseman, Jan 13 2019

Status

approved