Update:  I downloaded the sagemath tar.gz file, unpacked it, went into its 
directory, and typed "make."  It didn't take all day on my machine: maybe 
15 minutes.  Then I copied saga to python.  If I entered python, I got 
plain old python2.7.  If I entered ./python, sage loaded just as if I had 
entered ./sage, but only after a few bad starts with messages about 
SAGE_PATH.  Now sage loads quickly every time with ./python in the sage 
directory.

PyCharm steadfastly refused to accept sage as an interpreter, but did allow 
sage disguised as "python."  In PyCharm Tools / Run Python Console brought 
up the usual sage text.  I loaded sage math modules and it seemed I I had 
random() divisors() covered but these functions were not recognized.  On 
the sage command line, integer.divisors() yields all of the integer's 
divisors, which are only itself and 1 in the case of prime numbers.

So, sage is my PyCharm interpreter but the sage modules of interest, which 
seemed to load successfully, are not working.  Any suggestions?

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