Some Sums

Franklin T. Adams-Watters franktaw at
Sat Jul 30 03:04:19 CEST 2005

I'm trying to evaluate the following sums.  Can anybody produce more accurate results?

Number 1: sum_n=1^inf 1/sigma(n)^2
I get 1.306456[50]
(the digits in brackets I am not sure of).

Number 2: sum n=1^inf 1/sigma_2(n)
I get 1.537812[88]

Number 3: sum n=1^inf 1/phi(n)^2
In this case, I'm not entirely sure of any digits, but I think it's

For the first two, when you sum to N, the error is bounded by 1/N.

None of these is in the OEIS.
Franklin T. Adams-Watters
16 W. Michigan Ave.
Palatine, IL 60067

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