OFFSET
1,2
COMMENTS
Number of factorizations of n into factors (greater than 1) of 3 kinds.
LINKS
David A. Corneth, Table of n, a(n) for n = 1..10000
FORMULA
a(p^k) = A000716(k) for prime p.
EXAMPLE
From Antti Karttunen, Dec 15 2021: (Start)
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:
(8_3), (8_2), (8_1),
(4_3 * 2_3), (4_3 * 2_2), (4_3 * 2_1),
(4_2 * 2_3), (4_2 * 2_2), (4_2 * 2_1),
(4_1 * 2_3), (4_1 * 2_2), (4_1 * 2_1),
(2_3 * 2_3 * 2_3), (2_3 * 2_3 * 2_2), (2_3 * 2_3 * 2_1),
(2_3 * 2_2 * 2_2), (2_3 * 2_2 * 2_1), (2_3 * 2_1 * 2_1),
(2_2 * 2_2 * 2_2), (2_2 * 2_2 * 2_1), (2_2 * 2_1 * 2_1),
(2_1 * 2_1 * 2_1),
therefore a(8) = 22. (End)
PROG
(PARI) A339318list(n) = MultEulerT(vector(n, i, 3)); \\ Antti Karttunen, Jan 21 2022, using Andrew Howroyd's program given in A301830.
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Nov 30 2020
STATUS
approved