A167439 - OEIS

%I #4 Jul 05 2015 20:21:20

%S 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,

%T 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,

%U 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

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

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

%D 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)

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

%o (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 }

%Y Cf. A122651, A167439, A167865, A167866.

%K nonn

%O 0,4

%A _Max Alekseyev_, Nov 13 2009, Nov 15 2009