Gaussian Smoothness

Ed Pegg Jr edp at wolfram.com
Tue Jan 11 16:53:04 CET 2005


I rather like the sequence of adjacent smooth numbers.
http://www.research.att.com/cgi-bin/access.cgi/as/njas/sequences/eisA.cgi?Anum=A002072

I've been trying to extend that concept of smoothness.

I'll say that 7950+9650i is G6-smooth, since all of its prime Gaussian 
factors have real and imaginary parts ≤6.

Here are two large adjacent G5-smooth numbers.  These popped out after
a 4-week search.  I keep finding more, so I doubt very much that I've
found the actual "OEIS sequence"-worthy numbers.  The search is starting
to get more interesting, though.

28593+6426i = (1+2i)^5×(3)^3×(3+2i)×(5+2i)
28594+6426i = (1+i)^3×(1+4i)×(2+3i)×(4+i)^2×(5+4i)^2

--Ed Pegg Jr





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