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

%I A238950 #31 May 17 2025 05:30:47
%S A238950 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,
%T A238950 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,
%U A238950 2,6,1,9,1,2,4,4,2,6,1,7,2,2,1,10,2,2
%N A238950 Number of arcs from even to odd level vertices in divisor lattice D(n).
%H A238950 R. J. Mathar, <a href="/A238950/b238950.txt">Table of n, a(n) for n = 1..1000</a>
%H A238950 Sung-Hyuk 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 (see 11th line in Table 1).
%F A238950 a(n) = A062799(n) - A238951(n). - Eq. (2.37) [Cha] - _R. J. Mathar_, May 27 2017
%F A238950 a(n) = (A062799(n) + A358769(n))/2. - _Ridouane Oudra_, May 16 2025
%p A238950 read("transforms") :
%p A238950 omega := [seq(A001221(n), n=1..1000)] :
%p A238950 ones := [seq(1,n=1..1000)] :
%p A238950 a062799 := DIRICHLET(ones,omega) ;
%p A238950 for n from 1 do
%p A238950     a238951 := floor(op(n,a062799)/2) ;
%p A238950     a238950 := op(n,a062799)-floor(op(n,a062799)/2) ;
%p A238950     printf("%d %d\n",n,a238950) ;
%p A238950 end do: # _R. J. Mathar_, May 28 2017
%Y A238950 Cf. A062799, A038548, A358769.
%K A238950 nonn
%O A238950 1,6
%A A238950 _Sung-Hyuk Cha_, Mar 07 2014