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

1,3

Comments

A dual to A011772.

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.

Example

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.

Prog

(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

Crossrefs

Cf. A000217, A011772, A007843.

Sequence in context: A175892 A010783 A306680 * A032435 A337798 A117502

Adjacent sequences: A083309 A083310 A083311 * A083313 A083314 A083315

Keyword

nonn

Author

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

Extensions

More terms from Sam Alexander, Jan 03 2004

Status

approved