login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A327518
Number of factorizations of A302696(n), the n-th number that is 1, 2, or a nonprime number with pairwise coprime prime indices, into factors > 1 satisfying the same conditions.
0
1, 1, 2, 1, 3, 1, 2, 1, 1, 5, 2, 1, 4, 1, 2, 2, 7, 1, 1, 1, 1, 4, 2, 1, 7, 1, 2, 1, 4, 1, 5, 1, 11, 2, 2, 1, 2, 1, 2, 1, 7, 1, 1, 1, 4, 2, 1, 1, 1, 12, 2, 4, 1, 2, 7, 2, 1, 1, 10, 1, 1, 2, 15, 5, 1, 4, 2, 5, 1, 1, 1, 1, 1, 2, 4, 2, 1, 1, 12, 1, 2, 1, 1, 2, 2
OFFSET
1,3
EXAMPLE
The a(59) = 10 factorizations of 120 using the allowed factors, together with the corresponding multiset partitions of {1,1,1,2,3}:
(2*2*2*15) {{1},{1},{1},{2,3}}
(2*2*30) {{1},{1},{1,2,3}}
(2*4*15) {{1},{1,1},{2,3}}
(2*6*10) {{1},{1,2},{1,3}}
(2*60) {{1},{1,1,2,3}}
(4*30) {{1,1},{1,2,3}}
(6*20) {{1,2},{1,1,3}}
(8*15) {{1,1,1},{2,3}}
(10*12) {{1,3},{1,1,2}}
(120) {{1,1,1,2,3}}
MATHEMATICA
nn=100;
facsusing[s_, n_]:=If[n<=1, {{}}, Join@@Table[Map[Prepend[#, d]&, Select[facsusing[Select[s, Divisible[n/d, #]&], n/d], Min@@#>=d&]], {d, Select[s, Divisible[n, #]&]}]];
y=Select[Range[nn], #==1||CoprimeQ@@primeMS[#]&];
Table[Length[facsusing[Rest[y], n]], {n, y}]
CROSSREFS
See link for additional cross-references.
Sequence in context: A366833 A353161 A327533 * A174532 A089242 A349258
KEYWORD
nonn
AUTHOR
Gus Wiseman, Sep 19 2019
STATUS
approved