A318721 - OEIS

A318721

Number of strict relatively prime factorizations of n.

1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 2, 0, 1, 0, 1, 0, 4, 0, 0, 1, 1, 1, 2, 0, 1, 1, 2, 0, 4, 0, 1, 1, 1, 0, 2, 0, 1, 1, 1, 0, 2, 1, 2, 1, 1, 0, 6, 0, 1, 1, 0, 1, 4, 0, 1, 1, 4, 0, 4, 0, 1, 1, 1, 1, 4, 0, 2, 0, 1, 0, 6, 1, 1, 1

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OFFSET

1,24

COMMENTS

a(1) could be either 0 or 1.

LINKS

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

EXAMPLE

The a(60) = 6 factorizations are (3*20), (4*15), (5*12), (2*3*10), (2*5*6), (3*4*5).

MATHEMATICA

strfacs[n_]:=If[n<=1, {{}}, Join@@Table[(Prepend[#1, d]&)/@Select[strfacs[n/d], Min@@#1>d&], {d, Rest[Divisors[n]]}]];

Table[Length[Select[strfacs[n], GCD@@#==1&]], {n, 50}]