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 A189827 #13 May 27 2013 08:51:07
%S A189827 3,5,4,7,4,8,5,8,5,10,4,10,6,9,6,11,4,12,6,10,6,12,5,12,7,10,6,14,4,
%T A189827 14,6,10,8,13,6,13,6,12,6,16,4,14,8,10,8,14,5,16,7,12,6,14,6,16,8,12,
%U A189827 6,16,4,16,8,11,10,15,6,14,6,14,6,20,4,16,8,10,10
%N A189827 a(n) = d(n-1) + d(n+1), where d(k) is the number of divisors of k.
%C A189827 d(n-1) + d(n+1) is a measure of the compositeness of the numbers next to n. Sequence A189825 lists the first occurrence of each number.
%C A189827 It is conjectured that every number greater than 3 occurs an infinite number of times. Note that an infinite number of 4's is equivalent to there being an infinite number of twin primes (A001097). An infinite number of 5's is equivalent to there being an infinite number of primes of the form p^2-2 (A028871) or p^2+2 (A056899) for prime p. An infinite number of 6's is equivalent to there being an infinite number of primes of the form p^3-2 (A066878), p^3+2 (A048636), p*q-2 (A063637), or p*q+2 (A063638), where p and q are distinct primes.
%H A189827 T. D. Noe, <a href="/A189827/b189827.txt">Table of n, a(n) for n = 2..10000</a>
%e A189827 a(5) = d(4) + d(6) = 3 + 4 = 7.
%t A189827 Table[DivisorSigma[0,n-1] + DivisorSigma[0,n+1], {n, 2, 100}]
%t A189827 First[#]+Last[#]&/@Partition[DivisorSigma[0,Range[80]],3,1] (* _Harvey P. Dale_, May 27 2013 *)
%Y A189827 Cf. A175144, A189825.
%K A189827 nonn
%O A189827 2,1
%A A189827 _T. D. Noe_, Apr 28 2011