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%I #14 Mar 02 2023 16:52:41
%S 1,1,2,1,1,3,1,1,2,4,1,3,1,1,5,1,1,3,1,4,6,1,1,3,1,1,2,7,1,5,1,1,2,1,
%T 1,8,1,1,2,4,1,6,1,1,9,1,1,3,1,4,2,1,1,3,10,7,2,1,1,5,1,1,6,1,1,11,1,
%U 1,2,4,1,8,1,1,5,1,1,12,1,4,2,1,1,7,1,1,2,1,1,9,13,1,2,1,1,3,1,1,2,4,1,3,1
%N Largest integer m such that 1+2+...+m divides n.
%C A dual to A011772.
%H Antti Karttunen, <a href="/A083312/b083312.txt">Table of n, a(n) for n = 1..20000</a>
%H J. Sandor, <a href="http://www.gallup.unm.edu/~smarandache/Sandor43.pdf">On Additive Analogues of Certain Arithmetic Smarandache Functions</a>.
%H J. Sandor, <a href="http://www.gallup.unm.edu/~smarandache/JozsefSandor2.pdf">Geometric Theorems, Diophantine Equations, Arithmetic Functions</a>, American Research Press, 302 p., 2002.
%e ps(3) = 2 because 1+2 divides 3 and 2 is the largest such number.
%e ps(5) = 1 because 1 divides 5, while 1+2, 1+2+3 do not divide 5.
%o (PARI) a(n) = {m = 1; while ((t = m*(m+1)/2) <= n, if (n % t == 0, goodm = m); m ++;); goodm;} \\ _Michel Marcus_, Aug 12 2013
%Y Cf. A000217, A011772, A007843.
%K nonn
%O 1,3
%A K. Reddy (kakie(AT)indiainfo.com), Jun 03 2003
%E More terms from _Sam Alexander_, Jan 03 2004
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