Re: no prime number in the given range

"Tim Peters" <tim.one@xxxxxxxxxxx> writes:
[The Ghost In The Machine]
...
n1 = lcm(2,3,...,n) + 2
n2 = lcm(2,3,...,n) + n

where lcm is "least common multiple".

[Phil Carmody]
Aside - is there a common name for the function of n that has
value lcm(1..n)?

I don't think so, although it's a "very well-known function". See

http://www.research.att.com/~njas/sequences/A003418

The natural log of lcm(1..n) is often denoted via psi(n), as, e.g., in
equation (7) at:

For those perverts who prefer the real numbers to the integers! ;-)

http://mathworld.wolfram.com/ChebyshevFunctions.html

While it may be a display issue with my browser, equation (5) on the same
page /appears/ to be wrong. Should be:

psi(x) = sum over all i in 1 .. pi(x) of
k * ln(p_i) where
k is the largest integer such that (p_i)^k <= x

MW's correct - they've got a double sum. A sum of a single ln(p_i)
for each k such that ...

Phil
--
The man who is always worrying about whether or not his soul would be
damned generally has a soul that isn't worth a damn.
-- Oliver Wendell Holmes, Sr. (1809-1894), American physician and writer
.

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