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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
OFFSET
0,7
COMMENTS
Formally speaking, a(1) is not defined but letting a(1)=0 does not break any formula.
LINKS
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
KEYWORD
nonn
AUTHOR
Max Alekseyev, Nov 13 2009
STATUS
approved