Search: id:A133779
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%I A133779
%S A133779 1,0,1,3,4,1,5,6,1,7,4,8,1,3,9,5,10,1,11,6,12,1,13,7,14,1,3,5,15,4,8,16,
%T A133779 1,17,6,9,18,1,19,10,20,1,3,7,21,11,22,1,23,6,8,12,24,1,5,25,13,26,1,3,
%U A133779 9,27,4,7,14,28,1,29,10,15,30,1,31,4,8,16,32,1,3,11,33,17,34,1,5,7,35,
               6
%N A133779 Irregular array: n-th row lists the "isolated divisors" of n. A positive 
               divisor k of n is isolated if neither k-1 nor k+1 divides n.
%C A133779 The second term of the sequence, which corresponds to the second row 
               of the array, is 0 simply as a place-holder, since 2 has no isolated 
               divisors.
%C A133779 The number of terms in the n-th row of the array is A132881(n) (with 
               the exception of row 2, which has 0 elements, but is represented 
               here as 0).
%H A133779 Leroy Quet, <a href="http://www.prism-of-spirals.net/">Home Page</a> 
               (listed in lieu of email address)
%e A133779 The positive divisors of 20 are 1,2,4,5,10,20. Of these, 1 and 2 are 
               adjacent and 4 and 5 are adjacent. So the isolated divisors of 20 
               are 10 and 20.
%e A133779 Triangle begins:
%e A133779 1
%e A133779 -
%e A133779 1,3
%e A133779 4
%e A133779 1,5
%e A133779 6
%e A133779 1,7
%e A133779 4,8
%e A133779 1,3,9
%e A133779 5,10
%e A133779 1,11
%e A133779 6,12
%e A133779 1,13
%e A133779 7,14
%e A133779 1,3
%e A133779 5,15
%e A133779 4,8,16
%e A133779 ...
%p A133779 with(numtheory): a:=proc(n) local div,ISO,i: div:=divisors(n): ISO:={}: 
               for i to tau(n) do if member(div[i]-1, div)=false and member(div[i]+1, 
               div)=false then ISO:=`union`(ISO,{div[i]}) end if end do end proc: 
               1; 0; for j from 3 to 30 do seq(a(j)[i],i=1..nops(a(j)))end do; # 
               yields sequence in the form of an array - Emeric Deutsch (deutsch(AT)duke.poly.edu), 
               Oct 02 2007
%Y A133779 Cf. A133780, A132881, A132882.
%Y A133779 Sequence in context: A124446 A091542 A079529 this_sequence A137911 A019599 
               A114156
%Y A133779 Adjacent sequences: A133776 A133777 A133778 this_sequence A133780 A133781 
               A133782
%K A133779 nonn,tabf
%O A133779 1,4
%A A133779 Leroy Quet Sep 23 2007
%E A133779 More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Oct 02 2007
%E A133779 Extended by Ray Chandler (rayjchandler(AT)sbcglobal.net), Jun 24 2008

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