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

0,7

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

Formula

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

Prog

(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 }

Crossrefs

Cf. A122651, A167439, A167865.

Sequence in context: A164878 A319695 A029428 * A101422 A359938 A070304

Adjacent sequences: A167863 A167864 A167865 * A167867 A167868 A167869

Keyword

nonn

Author

Max Alekseyev, Nov 13 2009

Status

approved