{Spam?} Re: Possibly interesting sequence

[Don Reble]

> 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