Thread: Find the Value
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Old 2009-01-12, 01:48   #1
davar55
 
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May 2004
New York City

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Default Find the Value

It's well known that:
Product[prime p > 1]{1/(1-1/p^s)} = Sum[integer n > 0]{1/n^s} = zeta(s)
for real s > 1,
and also that for s=2 this equals pi^2 / 6.

Using this or any other way, find the value of the product
for s=2 if the primes > 1 are replaced by the composites > 1.

(This isn't hard.)

You'll find, for s=2, the product over primes > the product over composites.
Is this true for all values of s > 1, or is there some s where the two products are equal?
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