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A331048
Nearest integer to A001055(n)/A045778(n), where A001055 is factorizations and A045778 is strict factorizations.
4
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.
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.
Sequence in context: A037827 A086074 A180601 * A341593 A288636 A089723
KEYWORD
nonn,frac
AUTHOR
Gus Wiseman, Jan 10 2020
STATUS
approved