OFFSET
1,3
LINKS
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
KEYWORD
nonn
AUTHOR
Gus Wiseman, Sep 19 2019
STATUS
approved