[seqfan] Re: Sum 1/p log p

RGWv rgwv at rgwv.com
Mon Mar 26 16:09:44 CEST 2012

Et al,

    In "Mathematical Constants", Steven R. Finch, page 186-187, the sum 1/(p 
ln(p)) -> 1.6366163233… .

    While Erdos & Zhang proved that , for any primitive sequence, sum 1/(a_I 
ln(a_i)) < 1.84 and Clark strengthened this to < e^gamma.

    The estimate 1.6366163233… given here for the prime series is due to 

    That got me to https://oeis.org/A137245   Decimal expansion of sum 1/(p 
*log p) over the primes p=2,3,5,7,11,...

Hope this helps. Bob.

-----Original Message----- 
From: Charles Greathouse
Sent: Monday, March 26, 2012 2:43 AM
To: Sequence Fanatics Discussion list
Subject: [seqfan] Sum 1/p log p

Erdos (1989) conjectured that if a(1), a(2), ... is a sequence where
no term divides another, the sum of 1/(a(n) log a(n)) is at most sum
1/(p log p).  Is this constant in the OEIS? Is there a good way to
calculate it to high precision?

Charles Greathouse
Case Western Reserve University


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