

A167866


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


4



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
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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_{dn, d>1} a((nd)/d).


PROG

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


CROSSREFS

Cf. A122651, A167439, A167865
Sequence in context: A164878 A319695 A029428 * A101422 A070304 A275308
Adjacent sequences: A167863 A167864 A167865 * A167867 A167868 A167869


KEYWORD

nonn


AUTHOR

Max Alekseyev, Nov 13 2009


STATUS

approved



