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

1,4

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.

Links

Table of n, a(n) for n=1..87.

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}]

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.

Sequence in context: A037827 A086074 A180601 * A341593 A288636 A089723

Adjacent sequences: A331045 A331046 A331047 * A331049 A331050 A331051

Keyword

nonn,frac

Author

Gus Wiseman, Jan 10 2020

Status

approved