A167866 Length of the longest partition of n into distinct parts greater than 1, with each part divisible by the next one.

0, 0, 1, 1, 1, 1, 2, 1, 2, 2, 2, 1, 2, 1, 3, 2, 2, 1, 3, 1, 3, 3, 3, 1, 2, 2, 3, 3, 3, 1, 4, 1, 3, 3, 3, 3, 3, 1, 4, 3, 3, 1, 4, 1, 4, 4, 4, 1, 3, 3, 3, 3, 3, 1, 4, 3, 4, 4, 4, 1, 4, 1, 5, 4, 3, 3, 4, 1, 4, 4, 4, 1, 4, 1, 4, 4, 4, 3, 5, 1, 4, 4, 4, 1, 4, 3, 5, 4, 4, 1, 5, 3, 5, 5, 5, 4, 3, 1, 4, 4, 4, 1, 4, 1, 4

Offset: 0

Author

Max Alekseyev, Nov 13 2009

Keywords

• nonn

Comments

Formally speaking, a(1) is not defined but letting a(1)=0 does not break any formula.

Links

• Antti Karttunen, Table of n, a(n) for n = 0..16384

Crossrefs

Cf. A122651, A167439, A167865.

Programs

PARI

{ A167866(n) = local(r=0); if(n<=1,return(0)); fordiv(n,d, if(d>1, r=max(r,A167866((n-d)\d)); ); ); r+1 }

Formula

a(0) = a(1) = 0 and for n>=2, a(n) = 1 + max_{d|n, d>1} a((n-d)/d).