A364360 a(n) = dpf(n) ^ tpf(n), where dpf(n) is the number of distinct prime factors of n if n >= 2 and otherwise = 0; tpf(n) is the number of all prime factors of n if n >= 2 and otherwise = 0.

1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 4, 1, 8, 1, 4, 4, 1, 1, 8, 1, 8, 4, 4, 1, 16, 1, 4, 1, 8, 1, 27, 1, 1, 4, 4, 4, 16, 1, 4, 4, 16, 1, 27, 1, 8, 8, 4, 1, 32, 1, 8, 4, 8, 1, 16, 4, 16, 4, 4, 1, 81, 1, 4, 8, 1, 4, 27, 1, 8, 4, 27, 1, 32, 1, 4, 8, 8, 4, 27, 1, 32, 1

Offset: 0

Author

Peter Luschny, Jul 20 2023

Keywords

• nonn

Crossrefs

Cf. A263653, A363920, A001221, A001222.

Cf. A246655, A024619.

Programs

Maple

with(numtheory):
dpf := n -> ifelse(n = 0, 0, nops(factorset(n))): # dpf = [0] U [A001221].
tpf := n -> ifelse(n = 0, 0, bigomega(n)):        # tpf = [0] U [A001222].
A364360 := n -> dpf(n) ^ tpf(n):
seq(A364360(n), n = 0..81);

Formula

For n >= 2:

a(n) = 1 => a(n) in A246655, prime powers.

a(n) > 1 => a(n) in A024619, complement of A246655.