cp's OEIS Frontend

A360661 Number of factorizations of n into a prime number of factors > 1.

%I A360661 #24 Feb 16 2025 08:34:04
%S A360661 0,0,0,1,0,1,0,2,1,1,0,3,0,1,1,3,0,3,0,3,1,1,0,5,1,1,2,3,0,4,0,5,1,1,
%T A360661 1,7,0,1,1,5,0,4,0,3,3,1,0,9,1,3,1,3,0,5,1,5,1,1,0,9,0,1,3,7,1,4,0,3,
%U A360661 1,4,0,12,0,1,3,3,1,4,0,9,3,1,0,9,1,1,1,5,0,9,1,3,1,1,1,13,0,3,3,7
%N A360661 Number of factorizations of n into a prime number of factors > 1.
%C A360661 From _Bernard Schott_, Mar 25 2023: (Start)
%C A360661 a(n) depends only on the prime signature of n.
%C A360661 a(n) = 0 iff n is in A008578 (1 with primes).
%C A360661 a(n) = 1 iff n is in A001358 (semiprimes).
%C A360661 a(n) = 2 iff n is in A030078 (p^3).
%C A360661 a(n) = 3 iff n is in A080258 (p^4 or p*q^2).
%C A360661 a(n) = 4 iff n is in A007304 (p*q*r). (End)
%H A360661 Sean A. Irvine, <a href="https://github.com/archmageirvine/joeis/blob/master/src/irvine/oeis/a360/A360661.java">Java program</a> (github)
%H A360661 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/UnorderedFactorization.html">Unordered Factorization</a>
%F A360661 From _Bernard Schott_, Mar 25 2023: (Start)
%F A360661 a(A000040(n)) = 0.
%F A360661 a(A001248(n)) = a(A006881(n)) = 1.
%F A360661 a(A030514(n)) = a(A054753(n)) = 3. (End)
%e A360661 a(2) = 0 since 2 = 2 is the unique factorization of 2.
%e A360661 a(4) = 1 since 4 = 2^2 = 2 * 2.
%e A360661 a(6) = 1 since 6 = 2 * 3.
%e A360661 a(8) = 2 since 8 = 2^3 = 2 * 4 = 2 * 2 * 2.
%e A360661 a(12) = 3 since 12 = 3 * 2^2 = 2 * 6 = 3 * 4 = 2 * 2 * 3.
%e A360661 a(16) = 3 since 16 = 2^4 = 2 * 8 = 4 * 4 = 2 * 2 * 4.
%e A360661 a(30) = 4 since 30 = 2 * 3 * 5 = 2 * 15 = 3 * 10 = 5 * 6.
%Y A360661 Cf. A001055, A038499, A339890.
%Y A360661 Cf. A001248, A001358, A006881, A007304, A008578, A030078, A030514, A054753, A080258.
%K A360661 nonn
%O A360661 1,8
%A A360661 _Ilya Gutkovskiy_, Feb 15 2023