A060832

[franktaw at netscape.net]

This sequence has a formula a(n) = (e-1)*n + f(n) where A < f(n) < 0 ( with A > -4 ).  However, this is not correct.  If k is the largest value such that k!|n, a(n) - a(n-1) = k.  Then if f(n) < 0, f(n-1) < -k + e - 1, so f is unbounded in the negative direction.
 
The assertion that f(n) < 0 is clearly correct, since (e-1)*n = sum_{k=1}^{infinity} n/k! is term for term >= this sequence.
 
Franklin T. Adams-Watters
16 W. Michigan Ave.
Palatine, IL 60067
847-776-7645
 
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