A381399 a(n) is the number of prime elements in the set of bases and exponents in the prime factorization of n.

0, 1, 1, 1, 1, 2, 1, 2, 2, 2, 1, 2, 1, 2, 2, 1, 1, 2, 1, 2, 2, 2, 1, 2, 2, 2, 1, 2, 1, 3, 1, 2, 2, 2, 2, 2, 1, 2, 2, 3, 1, 3, 1, 2, 3, 2, 1, 2, 2, 2, 2, 2, 1, 2, 2, 3, 2, 2, 1, 3, 1, 2, 3, 1, 2, 3, 1, 2, 2, 3, 1, 2, 1, 2, 3, 2, 2, 3, 1, 2, 1, 2, 1, 3, 2, 2, 2, 3, 1, 3

Offset: 1

Author

Paolo Xausa, Feb 22 2025

Keywords

• nonn
• easy

Comments

Differs from A115588 at n = 64, 81, 256, 320, 405, 448, 512... = A381400.

Examples

			a(144) = 2 because the prime factorization of 144 is 2^4*3^2 and the set of these bases and exponents is {2, 3, 4}, containing 2 primes.
		

Links

• Paolo Xausa, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A115588, A381398, A381400, A381401.

Programs

Mathematica

A381399[n_] := Count[Union[Flatten[FactorInteger[n]]], _?PrimeQ];
Array[A381399, 100]