{Spam?} Re: Possibly interesting sequence
Don Reble
djr at nk.ca
Mon Aug 11 20:07:37 CEST 2008
> For a set S of positive integers, call n = SUM(k in S, k) good when
> SUM(k in S, 1/k) = 1. Which integers are good?
For a finite answer, ask which integers are bad. It's A051882.
If S is a multiset (k's may be repeated), it's A028229.
If we allow only odd k's, the multiset version (of "good" numbers)
begins:
1,9,25,33,41,49,57,65,73,81,89,97,105,113,121,129,137,145,153,
161,169,177,185,193,201,209
So far, it's the 8n+1 numbers, except that 17 is missing.
Exercise 1 (easy): prove that the sequence has infinitely many 8n+1
numbers.
Exercise 2 (easy, with the right insight): prove that the sequence
has only 8n+1 numbers.
Exercise 3: Alas, I don't know whether the sequence has all
sufficiently large 8n+1 numbers. Help?
See also R.K.Guy, "Unsolved Problems in Number Theory", D11.
--
Don Reble djr at nk.ca
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