A381401 a(n) is the number of (possibly non-distinct) prime elements in the multiset of bases and exponents in the prime factorization of n.

0, 1, 1, 2, 1, 2, 1, 2, 2, 2, 1, 3, 1, 2, 2, 1, 1, 3, 1, 3, 2, 2, 1, 3, 2, 2, 2, 3, 1, 3, 1, 2, 2, 2, 2, 4, 1, 2, 2, 3, 1, 3, 1, 3, 3, 2, 1, 2, 2, 3, 2, 3, 1, 3, 2, 3, 2, 2, 1, 4, 1, 2, 3, 1, 2, 3, 1, 3, 2, 3, 1, 4, 1, 2, 3, 3, 2, 3, 1, 2, 1, 2, 1, 4, 2, 2, 2, 3, 1, 4

Offset: 1

Author

Paolo Xausa, Feb 24 2025

Keywords

• nonn
• easy

Examples

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

Links

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

Crossrefs

Cf. A106490, A349281, A381398, A381399.

Programs

Mathematica

A381401[n_] := Count[FactorInteger[n], _?PrimeQ, {2}];
Array[A381401, 100]