A364360 - OEIS

%I #9 Jul 25 2023 16:04:54

%S 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,

%T 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,

%U 1,4,27,1,8,4,27,1,32,1,4,8,8,4,27,1,32,1

%N 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.

%F For n >= 2:

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

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

%p with(numtheory):

%p dpf := n -> ifelse(n = 0, 0, nops(factorset(n))): # dpf = [0] U [A001221].

%p tpf := n -> ifelse(n = 0, 0, bigomega(n)):        # tpf = [0] U [A001222].

%p A364360 := n -> dpf(n) ^ tpf(n):

%p seq(A364360(n), n = 0..81);

%Y Cf. A263653, A363920, A001221, A001222.

%Y Cf. A246655, A024619.

%K nonn

%O 0,7

%A _Peter Luschny_, Jul 20 2023