OFFSET
1,4
COMMENTS
LINKS
EXAMPLE
The a(74) = 9 factorizations of 84 together with the corresponding multiset partitions of {1,1,2,4}:
(2*2*3*7) {{1},{1},{2},{4}}
(2*3*14) {{1},{2},{1,4}}
(2*6*7) {{1},{1,2},{4}}
(2*42) {{1},{1,2,4}}
(3*4*7) {{2},{1,1},{4}}
(3*28) {{2},{1,1,4}}
(6*14) {{1,2},{1,4}}
(7*12) {{4},{1,1,2}}
(84) {{1,1,2,4}}
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||PrimeQ[#]||GCD@@PrimePi/@First/@FactorInteger[#]==1&];
Table[Length[facsusing[Rest[y], n]], {n, y}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Sep 17 2019
STATUS
approved