A167866 - OEIS

%I #9 Sep 23 2021 01:27:05

%S 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,

%T 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,

%U 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

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

%C Formally speaking, a(1) is not defined but letting a(1)=0 does not break any formula.

%H Antti Karttunen, <a href="/A167866/b167866.txt">Table of n, a(n) for n = 0..16384</a>

%F a(0) = a(1) = 0 and for n>=2, a(n) = 1 + max_{d|n, d>1} a((n-d)/d).

%o (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 }

%Y Cf. A122651, A167439, A167865.

%K nonn

%O 0,7

%A _Max Alekseyev_, Nov 13 2009