[seqfan] Typo in B-file for A063539

Allan Wechsler acwacw at gmail.com
Thu Apr 2 18:34:35 CEST 2020

A063539 collects numbers whose largest prime factor is less than the square
root. For example, 29925 = 3^2 * 5^2 * 7 * 19, and 19^2 is only 361, much
smaller than 29925.

An interesting feature of this sequence is that it has constant asymptotic
density; HAKMEM item 29 (Schroeppel) identifies the density as (1 - ln 2),
without proof.

Because of this intriguing feature, it's interesting to look at the graph
(which of course looks like a straight line), and this reveals an odd blot
under the line, which I have traced to a typo in the B-file.

A(7910) ought to be 29925 (the example I gave above), but is instead given
as 9925, which should not be in the sequence because its largest prime
factor is 397.

I wonder how typos like this can creep in -- the text of the B-file ought
to be copied directly from program output, and never pass through human
editorial hands which might drop a digit, as seems to have happened here.

(Also, the comments should include the slope of the line, ideally with a
citation to someplace that proves the identity.)

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