OFFSET
1,1
COMMENTS
From Tian Vlasic, Dec 31 2021: (Start)
Numbers that have an equal number of even and odd-length unordered factorizations.
There are infinitely many terms since p^2 is a term for prime p.
Out of all numbers of the form p^k with p prime (listed in A000961), only the numbers of the form p^2 (A001248) are terms.
Out of all numbers of the form p*q^k, p and q prime, only the numbers of the form p*q (A006881), p*q^2 (A054753), p*q^4 (A178739) and p*q^6 (A189987) are terms.
Similar methods can be applied to all prime signatures. (End)
LINKS
David A. Corneth, Table of n, a(n) for n = 1..10000
EXAMPLE
12 = 2*6 = 3*4 = 2*2*3 has an equal number of even-length factorizations and odd-length factorizations (2). - Tian Vlasic, Dec 09 2021
MATHEMATICA
facs[n_]:=If[n<=1, {{}}, Join@@Table[Map[Prepend[#, d]&, Select[facs[n/d], Min@@#>=d&]], {d, Rest[Divisors[n]]}]];
Join@@Position[Table[Sum[(-1)^Length[f], {f, facs[n]}], {n, 100}], 0]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Gus Wiseman, Sep 15 2018
STATUS
approved