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

1,6

Comments

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

Links

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

Example

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.

Mathematica

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

Crossrefs

Cf. A115588, A381398, A381400, A381401.

Sequence in context: A164885 A084989 A128538 * A115588 A240471 A263569

Adjacent sequences: A381396 A381397 A381398 * A381400 A381401 A381402

Keyword

nonn,easy

Author

Paolo Xausa, Feb 22 2025

Status

approved