cp's OEIS Frontend

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.

%I A364360 #9 Jul 25 2023 16:04:54
%S A364360 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 A364360 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 A364360 1,4,27,1,8,4,27,1,32,1,4,8,8,4,27,1,32,1
%N 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.
%F A364360 For n >= 2:
%F A364360 a(n) = 1 => a(n) in A246655, prime powers.
%F A364360 a(n) > 1 => a(n) in A024619, complement of A246655.
%p A364360 with(numtheory):
%p A364360 dpf := n -> ifelse(n = 0, 0, nops(factorset(n))): # dpf = [0] U [A001221].
%p A364360 tpf := n -> ifelse(n = 0, 0, bigomega(n)):        # tpf = [0] U [A001222].
%p A364360 A364360 := n -> dpf(n) ^ tpf(n):
%p A364360 seq(A364360(n), n = 0..81);
%Y A364360 Cf. A263653, A363920, A001221, A001222.
%Y A364360 Cf. A246655, A024619.
%K A364360 nonn
%O A364360 0,7
%A A364360 _Peter Luschny_, Jul 20 2023