# Centerless Polygons

f n=sum[0^mod n q|a<-[3..n],q<-[a,3*a..n]]


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51 bytes

f n=sum[1|a<-[3..n],b<-[1,3..n],c<-[1..n],a*b*c==n]


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The output is the number of ways to factor $$\n=abc\$$ into three positive factors, where $$\a \geq 3\$$, $$\b\$$ is odd, and $$\c\$$ is unconstrained.

## 05AB1E, 1716 10 bytes

3÷ÝsÑÃÑÉOO


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3÷L         Get a list from 0 to n//3.
sÑÃ      Keep only factors of n.
ÑÉO   Number of odd divisors of each factor.
O  Output the sum.


## J, 29 bytes

[:+/@,[=[+/\\[email protected](*1+i.)~"+3+i.


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[:+/@,[=[+/\\[email protected](*1+i.)~"+3+i.
i. 0…N-1
3+   3…N+2
"+     for each y in 3…N+2:
[      (*1+i.)~       y * 0…N, thus f.e. 5 10 15 20 … for p_5
\\[email protected]               take every possible sublist
+/                   and sum it
[=                      which sums are equal to N?
[:+/@,                        count the true bits