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

1,4

Links

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

Example

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.

Mathematica

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

Crossrefs

Cf. A106490, A349281, A381398, A381399.

Sequence in context: A128428 A056171 A357328 * A395811 A333749 A238949

Adjacent sequences: A381398 A381399 A381400 * A381402 A381403 A381404

Keyword

nonn,easy

Author

Paolo Xausa, Feb 24 2025

Status

approved