login
Maximal level size of arcs in divisor lattice D(n).
3

%I #27 Mar 28 2020 20:00:31

%S 0,1,1,1,1,2,1,1,1,2,1,3,1,2,2,1,1,3,1,3,2,2,1,3,1,2,1,3,1,6,1,1,2,2,

%T 2,4,1,2,2,3,1,6,1,3,3,2,1,3,1,3,2,3,1,3,2,3,2,2,1,7,1,2,3,1,2,6,1,3,

%U 2,6,1,5,1,2,3,3,2,6,1,3,1,2

%N Maximal level size of arcs in divisor lattice D(n).

%C A divisor d of n has level given by bigomega(d) and in-degree given by omega(d). The number of arcs on a level is the sum of the in-degrees of all divisors on the level. - _Andrew Howroyd_, Mar 28 2020

%H Andrew Howroyd, <a href="/A238946/b238946.txt">Table of n, a(n) for n = 1..1000</a> (terms 1..200 from Sung-Hyuk Cha)

%H S.-H. Cha, E. G. DuCasse, and L. V. Quintas, <a href="http://arxiv.org/abs/1405.5283">Graph Invariants Based on the Divides Relation and Ordered by Prime Signatures</a>, arXiv:1405.5283 [math.NT], 2014.

%o (PARI) a(n)={if(n==1, 0, my(v=vector(bigomega(n))); fordiv(n, d, if(d>1, v[bigomega(d)] += omega(d))); vecmax(v))} \\ _Andrew Howroyd_, Mar 28 2020

%Y Cf. A001221 (omega), A001222 (bigomega), A062799, A096825, A238955, A238968.

%K nonn

%O 1,6

%A _Sung-Hyuk Cha_, Mar 07 2014

%E a(1) corrected by _Andrew Howroyd_, Mar 28 2020