A238950 Number of arcs from even to odd level vertices in divisor lattice D(n).

0, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 4, 1, 2, 2, 2, 1, 4, 1, 4, 2, 2, 1, 5, 1, 2, 2, 4, 1, 6, 1, 3, 2, 2, 2, 6, 1, 2, 2, 5, 1, 6, 1, 4, 4, 2, 1, 7, 1, 4, 2, 4, 1, 5, 2, 5, 2, 2, 1, 10, 1, 2, 4, 3, 2, 6, 1, 4, 2, 6, 1, 9, 1, 2, 4, 4, 2, 6, 1, 7, 2, 2, 1, 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 11th line in Table 1).

Crossrefs

Cf. A062799, A038548, 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) ;
    a238950 := op(n,a062799)-floor(op(n,a062799)/2) ;
    printf("%d %d\n",n,a238950) ;
end do: # R. J. Mathar, May 28 2017

Formula

a(n) = A062799(n) - A238951(n). - Eq. (2.37) [Cha] - R. J. Mathar, May 27 2017

a(n) = (A062799(n) + A358769(n))/2. - Ridouane Oudra, May 16 2025