A238951 The number of arcs from odd to even level vertices in divisor lattice D(n).

0, 0, 0, 1, 0, 2, 0, 1, 1, 2, 0, 3, 0, 2, 2, 2, 0, 3, 0, 3, 2, 2, 0, 5, 1, 2, 1, 3, 0, 6, 0, 2, 2, 2, 2, 6, 0, 2, 2, 5, 0, 6, 0, 3, 3, 2, 0, 6, 1, 3, 2, 3, 0, 5, 2, 5, 2, 2, 0, 10, 0, 2, 3, 3, 2, 6, 0, 3, 2, 6, 0, 8, 0, 2, 3, 3, 2, 6, 0, 6, 2, 2, 0, 10, 2, 2

Offset: 1

Author

Sung-Hyuk Cha, Mar 07 2014

Keywords

• nonn

Links

• R. J. Mathar, Table of n, a(n) for n = 1..1000
• Sung-Hyuk 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 (see 12th line in Table 1).

Crossrefs

Cf. A056924, A062799, A238950, A358769.

Programs

Maple

read("transforms"):
omega := [seq(A001221(n), n=1..1000)] ;
ones := [seq(1,n=1..1000)] ;
a062799 := DIRICHLET(ones,omega) ;
for n from 1 do
    a238951 := floor(op(n,a062799)/2) ;
    printf("%d %d\n",n,a238951) ;
end do: # R. J. Mathar, May 28 2017

Formula

a(n) = A062799(n) - A238950(n) = floor(A062799(n)/2). [Cha eqs. (2.34), (2.37)]

a(n) = (A062799(n) - A358769(n))/2. - Ridouane Oudra, May 17 2025