This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A132747 #20 Mar 22 2024 06:49:09
%S A132747 0,2,0,2,0,3,0,2,0,2,0,4,0,2,0,2,0,3,0,4,0,2,0,4,0,2,0,2,0,5,0,2,0,2,
%T A132747 0,4,0,2,0,4,0,5,0,2,0,2,0,4,0,2,0,2,0,3,0,4,0,2,0,6,0,2,0,2,0,3,0,2,
%U A132747 0,2,0,6,0,2,0,2,0,3,0,4,0,2,0,6,0,2,0,2,0,7,0,2,0,2,0,4,0,2,0,4,0,3,0,2,0
%N A132747 a(n) = number of non-isolated divisors of n.
%C A132747 A divisor d of n is non-isolated if either d-1 or d+1 divides n. a(2n-1) = 0 for all n >= 1.
%H A132747 Ray Chandler, <a href="/A132747/b132747.txt">Table of n, a(n) for n=1..10000</a>
%F A132747 a(n) = A000005(n) - A132881(n).
%F A132747 Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = log(2) + 1 = A002162 + 1 = 1.693147.... . - _Amiram Eldar_, Mar 22 2024
%e A132747 The positive divisors of 20 are 1,2,4,5,10,20. Of these, 1 and 2 are next to each other and 4 and 5 are next to each other. So a(20) = the number of these divisors, which is 4.
%t A132747 Table[Length[Select[Divisors[n], If[ # > 1, IntegerQ[n/(#*(# - 1))]] || IntegerQ[n/(#*(# + 1))] &]], {n, 1, 90}] (* _Stefan Steinerberger_, Oct 26 2007 *)
%o A132747 (PARI) a(n) = my(div = divisors(n)); sumdiv(n, d, vecsearch(div, d-1) || vecsearch(div, d+1)); \\ _Michel Marcus_, Aug 22 2014
%Y A132747 Cf. A000005, A002162, A129308, A132748, A132881.
%K A132747 nonn
%O A132747 1,2
%A A132747 _Leroy Quet_, Aug 27 2007
%E A132747 More terms from _Stefan Steinerberger_, Oct 26 2007
%E A132747 Extended by _Ray Chandler_, Jun 24 2008