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A167439
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Length of the longest partition of n into distinct parts, with each part divisible by the next one.
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4
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0, 1, 1, 2, 2, 2, 2, 3, 2, 3, 3, 3, 2, 3, 3, 4, 3, 3, 3, 4, 3, 4, 4, 4, 2, 3, 3, 4, 4, 4, 4, 5, 3, 4, 4, 4, 4, 4, 4, 5, 4, 4, 4, 5, 4, 5, 5, 5, 3, 4, 4, 4, 4, 4, 4, 5, 4, 5, 5, 5, 4, 5, 5, 6, 5, 4, 4, 5, 4, 5, 5, 5, 4, 5, 4, 5, 5, 5, 5, 6, 4, 5, 5, 5, 4, 5, 5, 6, 5, 5, 5, 6, 5, 6, 6, 6, 5, 4, 4, 5, 5, 5, 4, 5, 4
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OFFSET
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0,4
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COMMENTS
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a(n) > sqrt(log(n))/2.
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REFERENCES
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V. A. Sadovnichiy, A. A. Grigoryan and S. V. Konyagin (1987), "Problems of mathematical olympiads for university students". Section 4.1, problem 25. (in Russian)
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LINKS
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Table of n, a(n) for n=0..104.
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FORMULA
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a(n) = max{ A167866(n), A167866(n-1) + 1 }.
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PROG
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(PARI) { a(n, m=0) = local(r=0); if(n==0, return(0)); fordiv(n, d, if(d<=m, next); r=max(r, 1+a((n-d)\d, 1)) ); r }
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CROSSREFS
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Cf. A122651, A167439, A167865, A167866.
Sequence in context: A068211 A236832 A089050 * A272314 A241216 A125173
Adjacent sequences: A167436 A167437 A167438 * A167440 A167441 A167442
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KEYWORD
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nonn
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AUTHOR
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Max Alekseyev, Nov 13 2009, Nov 15 2009
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STATUS
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approved
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