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 A200213 #41 Oct 24 2024 03:52:03
%S A200213 0,0,0,0,0,2,0,2,0,2,0,4,0,2,2,2,0,4,0,4,2,2,0,6,0,2,2,4,0,6,0,4,2,2,
%T A200213 2,6,0,2,2,6,0,6,0,4,4,2,0,8,0,4,2,4,0,6,2,6,2,2,0,10,0,2,4,4,2,6,0,4,
%U A200213 2,6,0,10,0,2,4,4,2,6,0,8,2,2,0,10,2
%N A200213 Ordered factorizations of n with 2 distinct parts, both > 1.
%H A200213 Antti Karttunen, <a href="/A200213/b200213.txt">Table of n, a(n) for n = 1..10000</a>
%H A200213 Arnold Knopfmacher and Michael Mays, <a href="http://www.mathematica-journal.com/issue/v10i1/contents/Factorizations/Factorizations_3.html">Ordered and Unordered Factorizations of Integers</a>, The Mathematica Journal, Vol 10 (1).
%F A200213 From _Antti Karttunen_, Jul 07 & Jul 09 2017: (Start)
%F A200213 a(1) = 0; for n > 1, a(n) = A000005(n) - A010052(n) - 2.
%F A200213 For n >= 2, a(n) = A161840(n) - 2*A010052(n). (End)
%e A200213 a(24) = 6 = card({{2,12},{3,8},{4,6},{6,4},{8,3},{12,2}}).
%p A200213 a := n -> `if`(n<2, 0, numtheory:-tau(n) - `if`(issqr(n), 3, 2)):
%p A200213 seq(a(n), n = 1..85); # _Peter Luschny_, Jul 10 2017
%t A200213 OrderedFactorizations[1] = {{}}; OrderedFactorizations[n_?PrimeQ] := {{n}}; OrderedFactorizations[n_] := OrderedFactorizations[n] = Flatten[Function[d, Prepend[#, d] & /@ OrderedFactorizations[n/d]] /@ Rest[Divisors[n]], 1]; a[n_] := With[{of2 = Sort /@ Select[OrderedFactorizations[n], Length[#] == 2 && Length[# // Union] == 2 &] // Union}, Length[Permutations /@ of2 // Flatten[#, 1] &]]; Table[a[n], {n, 1, 85}] (* _Jean-François Alcover_, Jul 02 2013, copied and adapted from The Mathematica Journal *)
%o A200213 (PARI) A200213(n) = if(!n,n,sumdiv(n, d, (d<>(n/d))*(d>1)*(d<n))); \\ _Antti Karttunen_, Jul 07 2017
%o A200213 (PARI) a(n) = if (n==1, 0, numdiv(n) - issquare(n) - 2); \\ _Michel Marcus_, Jul 07 2017
%o A200213 (Scheme) (define (A200213 n) (if (<= n 1) 0 (- (A000005 n) 2 (A010052 n)))) ;; _Antti Karttunen_, Jul 07 2017
%Y A200213 Cf. A000005, A010052, A070824, A161840, A200214, A211159.
%K A200213 nonn,easy
%O A200213 1,6
%A A200213 _Peter Luschny_, Nov 14 2011
%E A200213 Description clarified and term a(0) removed by _Antti Karttunen_, Jul 09 2017