Maybe the fact that prod (sin^2(n) - 25/16) stays bounded and diverges has something to do with this.

This suggests that Maybe we should replace s with similar to make things nicer.

Im also unsure about that integral ... Maybe the values of F are too close to 0 most of the time.

I think with strong hesitation that for large n with respect to x ,

The function F Goes to exp(-2n ln(n) + 2n) prod gamma(p_n)^(2/p_n) asymptotically with measure 1. This estimate is based on statistical thinking and prod p_n ~ exp(n ln n - n).

This estimate hints at correcting factors for the integrand also known as weights.

Atthough all this suggests we are not talking of the simplest or best sieve type function , it is intuïtive and therefore intresting.

A lot of work to do but lots of inspiration.

The way i like math usually.

Regards

Tommy1729

This suggests that Maybe we should replace s with similar to make things nicer.

Im also unsure about that integral ... Maybe the values of F are too close to 0 most of the time.

I think with strong hesitation that for large n with respect to x ,

The function F Goes to exp(-2n ln(n) + 2n) prod gamma(p_n)^(2/p_n) asymptotically with measure 1. This estimate is based on statistical thinking and prod p_n ~ exp(n ln n - n).

This estimate hints at correcting factors for the integrand also known as weights.

Atthough all this suggests we are not talking of the simplest or best sieve type function , it is intuïtive and therefore intresting.

A lot of work to do but lots of inspiration.

The way i like math usually.

Regards

Tommy1729