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 A323326 #13 Jan 11 2019 07:57:48 %S A323326 2,3,2,2,1,1,0,2,4,4,3,5,4,4,4,4,3,5,4,4,4,4,3,5,5,5,5,5,4,4,3,3,3,3, %T A323326 3,5,4,4,4,6,5,5,4,4,4,4,3,3,3,3,3,3,2,2,2,4,4,4,3,5,4,4,4,4,4,4,3,3, %U A323326 3,3,2,4,3,3,3,3,3,3,2,4,4,4,3,5,5,5,5,7,6,6,6,6,6,6,6,8,7,7,7,7,6,6,5,7,7,7,6,8,7,7,7,7,6,6,6,6,6,6,6,6,6,6,6 %N A323326 a(n) = 2*T(n) - pi(n), where T(n) (A208251) is the number of refactorable/tau numbers (A033950) <= n and pi(n) (A000720) is the number of primes <= n. %C A323326 Colton conjectured that T(n) >= pi(n)/2 for all n, i.e., this sequence is nonnegative. Zelinsky proved it for n > 7.42*10^13 (see the Zelinsky reference). This calculation went to 7.44*10^13, proving the conjecture. %H A323326 Simon Colton, <a href="https://cs.uwaterloo.ca/journals/JIS/colton/joisol.html">Refactorable Numbers - A Machine Invention</a>, J. Integer Sequences, Vol. 2, 1999. %H A323326 Joshua Zelinsky, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL5/Zelinsky/zelinsky9.html">Tau Numbers: A Partial Proof of a Conjecture and Other Results </a>, Journal of Integer Sequences, Vol. 5 (2002), Article 02.2.8. %e A323326 For n=6, pi(6)=3, T(6)=2, so a(6) = 2*2 - 3 = 1. %Y A323326 Cf. A033950, A208251, A000720. %K A323326 nonn %O A323326 1,1 %A A323326 _Jud McCranie_, Jan 11 2019