cp's OEIS Frontend

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.

%I A133779 #19 May 17 2023 15:15:17
%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,
%T A133779 16,1,17,6,9,18,1,19,10,20,1,3,7,21,11,22,1,23,6,8,12,24,1,5,25,13,26,
%U A133779 1,3,9,27,4,7,14,28,1,29,10,15,30,1,31,4,8,16,32,1,3,11,33,17,34,1,5,7,35,6
%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 placeholder, 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 Michael De Vlieger, <a href="/A133779/b133779.txt">Table of n, a(n) for n = 1..12248</a> (Rows 1 <= n <= 2000).
%H A133779 <a href="/index/Di#divisors">Index entries for sequences related to divisors of numbers</a>
%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 1,3,5,15
%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_, Oct 02 2007
%t A133779 Table[Select[Divisors@ n, NoneTrue[# + {-1 + 2 Boole[# == 1], 1}, Divisible[n, #] &] &] /. {} -> {0}, {n, 36}] // Flatten (* _Michael De Vlieger_, Aug 19 2017 *)
%Y A133779 Cf. A133780, A132881, A132882.
%K A133779 nonn,tabf,easy
%O A133779 1,4
%A A133779 _Leroy Quet_, Sep 23 2007
%E A133779 More terms from _Emeric Deutsch_, Oct 02 2007
%E A133779 Extended by _Ray Chandler_, Jun 24 2008