A083312 Largest integer m such that 1+2+...+m divides n.

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, 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, 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

Offset: 1

Author

K. Reddy (kakie(AT)indiainfo.com), Jun 03 2003

Keywords

• nonn

Comments

A dual to A011772.

Examples

			ps(3) = 2 because 1+2 divides 3 and 2 is the largest such number.
ps(5) = 1 because 1 divides 5, while 1+2, 1+2+3 do not divide 5.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000
• J. Sandor, On Additive Analogues of Certain Arithmetic Smarandache Functions.
• J. Sandor, Geometric Theorems, Diophantine Equations, Arithmetic Functions, American Research Press, 302 p., 2002.

Crossrefs

Cf. A000217, A011772, A007843.

Programs

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

Extensions

More terms from Sam Alexander, Jan 03 2004