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 A063450 #24 Mar 08 2025 06:00:41 %S A063450 2,3,4,6,8,9,10,12,14,15,16,18,20,21,22,24,25,26,27,28,30,32,33,34,36, %T A063450 38,40,42,44,45,46,48,50,51,52,54,56,57,58,60,62,63,64,66,68,70,72,74, %U A063450 75,76,78,80,81,82,84,85,86,88,90,91,92,93,94,96,98,99,100,102,104,105 %N A063450 Numbers k such that d(k+1) < 2*d(k), where d() is the number of divisors function A000005. %H A063450 Amiram Eldar, <a href="/A063450/b063450.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from Harry J. Smith) %e A063450 d(k+1) < 2*d(k) holds mainly for composites and for the primes 2 and 3. E.g.: %e A063450 For k = 10: 2*d(10) = 2*4 = 8 > 2 = d(11). %e A063450 For k = 3: 2*d(3) = 2*2 = 4 > d(4) = 3. %e A063450 For k = 2: 2*d(2) = 2*2 = 4 > d(3) = 2. %t A063450 SequencePosition[DivisorSigma[0,Range[110]],_?(#[[2]]<2#[[1]]&)][[All,1]]// Quiet (* _Harvey P. Dale_, Aug 19 2020 *) %o A063450 (PARI) is(m) = numdiv(m + 1) < 2*numdiv(m); \\ _Harry J. Smith_, Aug 21 2009 %Y A063450 Cf. A000005, A002808, A063446, A063449. %K A063450 nonn %O A063450 1,1 %A A063450 _Labos Elemer_, Jul 24 2001 %E A063450 Formatting by _Charles R Greathouse IV_, Mar 24 2010