[seqfan] Re: Question about A003592.

[Frank Adams-Watters]

The sums of the reciprocals of numbers p_1^i_1 * p_2^i_2 * ... * 
p_k^i_k is the product p_1/(p_1-1) * p_2/(p_2-1) * ... * p_k/(p_k-1). 
The sequence factors into parts 1, p_j, p_j^2, ....

Franklin T. Adams-Watters

-----Original Message-----
From: L. Edson Jeffery <lejeffery2 at gmail.com>
To: seqfan <seqfan at list.seqfan.eu>
Sent: Mon, Jul 7, 2014 1:07 pm
Subject: [seqfan] Question about A003592.


A003592 = {numbers of the form 2^i*5^j, with i, j >= 0} = {1, 2, 4, 5, 
8,
10, 16, 20, 25, 32, 40, 50, 64, 80, 100, ...}.

In A003592 David Wasserman states that each 1/A003592(n) has terminating
decimal expansion. He gave no references, so I assume that he has worked
out a proof. Then it follows that

(1) sum_{k=1..n} 1/A003592(k)

is terminating. The partial sums (1) seem to be converging, so I wonder:
can someone compute the limit as n -> infinity?

Ed Jeffery

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