A331048 Nearest integer to A001055(n)/A045778(n), where A001055 is factorizations and A045778 is strict factorizations.

1, 1, 1, 2, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1

Offset: 1

Author

Gus Wiseman, Jan 10 2020

Keywords

• nonn
• frac

Comments

A factorization of n is a finite, nondecreasing sequence of positive integers > 1 with product n. It is strict if the factors are all different.

Crossrefs

The exact quotient is A331023/A331024.

The same for integer partitions is A330996 ~ A330994/A330995.

Cf. A001055, A001222, A002033, A005117, A045778, A045779, A045780, A045782, A045783, A330972, A330977, A330991.

Programs

Mathematica

facs[n_]:=If[n<=1,{{}},Join@@Table[Map[Prepend[#,d]&,Select[facs[n/d],Min@@#>=d&]],{d,Rest[Divisors[n]]}]];
Table[Round[Length[facs[n]]/Length[Select[facs[n],UnsameQ@@#&]]],{n,100}]