This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A339318 #19 Jan 27 2022 21:15:22
%S A339318 1,3,3,9,3,12,3,22,9,12,3,39,3,12,12,51,3,39,3,39,12,12,3,105,9,12,22,
%T A339318 39,3,57,3,108,12,12,12,135,3,12,12,105,3,57,3,39,39,12,3,258,9,39,12,
%U A339318 39,3,105,12,105,12,12,3,201,3,12,39,221,12,57,3,39,12,57
%N A339318 Dirichlet g.f.: Product_{k>=2} 1 / (1 - k^(-s))^3.
%C A339318 Number of factorizations of n into factors (greater than 1) of 3 kinds.
%H A339318 David A. Corneth, <a href="/A339318/b339318.txt">Table of n, a(n) for n = 1..10000</a>
%F A339318 a(p^k) = A000716(k) for prime p.
%e A339318 From _Antti Karttunen_, Dec 15 2021: (Start)
%e A339318 For n = 8, A001055(8) = 3, as it has three ordinary factorizations: (8), (4*2), (2*2*2). When allowing each of the factors appear in three different guises (here indicated with a subscript), and where neither the order of factors nor their subscripts matter, we get the following 22 different factorizations:
%e A339318 (8_3), (8_2), (8_1),
%e A339318 (4_3 * 2_3), (4_3 * 2_2), (4_3 * 2_1),
%e A339318 (4_2 * 2_3), (4_2 * 2_2), (4_2 * 2_1),
%e A339318 (4_1 * 2_3), (4_1 * 2_2), (4_1 * 2_1),
%e A339318 (2_3 * 2_3 * 2_3), (2_3 * 2_3 * 2_2), (2_3 * 2_3 * 2_1),
%e A339318 (2_3 * 2_2 * 2_2), (2_3 * 2_2 * 2_1), (2_3 * 2_1 * 2_1),
%e A339318 (2_2 * 2_2 * 2_2), (2_2 * 2_2 * 2_1), (2_2 * 2_1 * 2_1),
%e A339318 (2_1 * 2_1 * 2_1),
%e A339318 therefore a(8) = 22. (End)
%o A339318 (PARI) A339318list(n) = MultEulerT(vector(n, i, 3)); \\ _Antti Karttunen_, Jan 21 2022, using _Andrew Howroyd_'s program given in A301830.
%Y A339318 Cf. A000716, A001055, A301830, A339319, A339320, A339321, A339322, A339323, A339324.
%K A339318 nonn
%O A339318 1,2
%A A339318 _Ilya Gutkovskiy_, Nov 30 2020