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

Author

Gus Wiseman, Jan 13 2019

Keywords

• nonn

Comments

a(1) = 1 by convention.

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

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.

Programs

Mathematica

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

PARI

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

Formula

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