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.SSSEC(Schematic Diagram of the Development)

.BEGIN SELECT 8 NOFILL PREFACE 0 MILLS TURN OFF "α↑↓" INDENT 12


		         Divisors-of
 		           /
		          /
		         /  ⊗4Look for extremals⊗*
		 (very few divisors)
		       /
		      /
		     /
		  Primes
		    /\
		   /  \
		  /    \
		 /      \
		/	 \
  	    ⊗4Found some connections⊗*
	   (to ADD-1-)	 (to TIMES-1-)
	     / 		     \
	    /		      \
	Goldbach⊗1'⊗*s           Unique 
	Conjecture	  Factorization

.END APART

.ONCE PREFACE 2

This little picture  symbolizes the reasoning behind the  three major
concepts  derived in the  example.  The  italicized phrases labelling
the  arcs  represent  the  key  heuristics  used  in   the  plausible
reasoning; the  nodes represent  the concepts (or  the relationships)
discovered and worked on.

The reader may notice that a bilateral symmetry  is missing: what about numbers
with "very many" divisors, instead of "very few"? AM doggedly thought
that such numbers might be very interesting, and eventually hinted at
what  is  probably  the   first  explicit  characterization  of  such
numbers$$  See Section {[2] MAXDIVSEC}.{[1] MAXDIVSSEC}, on page {[3]
MAXDIVPAGE}.  These  are  the  so-called  "highly-composite"  numbers  of
Ramanujan.   They  are the  local maxima  of the  function  d(n), the
number of divisors of  n.  Prior to  "AM's conjecture", most work  on
d(n) was  not  in characterizing  its maxima,  but  rather, e.g.,  in
finding its max order, normal order, etc. $.