A238946 Maximal level size of arcs in divisor lattice D(n).

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, 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, 2, 6, 1, 5, 1, 2, 3, 3, 2, 6, 1, 3, 1, 2

Offset: 1

Author

Sung-Hyuk Cha, Mar 07 2014

Keywords

• nonn

Comments

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

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..1000 (terms 1..200 from Sung-Hyuk Cha)
• S.-H. Cha, E. G. DuCasse, and L. V. Quintas, Graph Invariants Based on the Divides Relation and Ordered by Prime Signatures, arXiv:1405.5283 [math.NT], 2014.

Crossrefs

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

Programs

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

Extensions

a(1) corrected by Andrew Howroyd, Mar 28 2020