A167439 Length of the longest partition of n into distinct parts, with each part divisible by the next one.

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

Offset

0,4

Comments

a(n) > sqrt(log(n))/2.

References

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)

Links

Table of n, a(n) for n=0..104.

Formula

a(n) = max{ A167866(n), A167866(n-1) + 1 }.

Prog

(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 }

Crossrefs

Cf. A122651, A167439, A167865, A167866.

Sequence in context: A068211 A236832 A089050 * A272314 A241216 A125173

Adjacent sequences: A167436 A167437 A167438 * A167440 A167441 A167442

Keyword

nonn

Author

Max Alekseyev, Nov 13 2009, Nov 15 2009

Status

approved