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A238972 The number of arcs from even to odd level vertices in divisor lattice in canonical order.

%I A238972 #15 Mar 28 2020 17:48:53
%S A238972 0,1,1,2,2,4,6,2,5,6,10,16,3,7,9,14,17,26,40,3,8,11,18,12,23,36,27,42,
%T A238972 64,96,4,10,14,22,16,30,46,32,38,58,88,68,102,152,224,4,11,16,26,19,
%U A238972 36,56,20,41,48,74,112,52,80,93,140,208,108,162,240,352,512
%N A238972 The number of arcs from even to odd level vertices in divisor lattice in canonical order.
%H A238972 Andrew Howroyd, <a href="/A238972/b238972.txt">Table of n, a(n) for n = 0..2713</a> (rows 0..20)
%H A238972 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.
%F A238972 From _Andrew Howroyd_, Mar 28 2020: (Start)
%F A238972 T(n,k) = A238950(A063008(n,k)).
%F A238972 T(n,k) = A238964(n,k) - A238973(n,k).
%F A238972 T(n,k) = ceiling(A238964(n,k)/2). (End)
%e A238972 Triangle T(n,k) begins:
%e A238972   0;
%e A238972   1;
%e A238972   1, 2;
%e A238972   2, 4,  6;
%e A238972   2, 5,  6, 10, 16;
%e A238972   3, 7,  9, 14, 17, 26, 40;
%e A238972   3, 8, 11, 18, 12, 23, 36, 27, 42, 64, 96;
%e A238972   ...
%p A238972 with(numtheory):
%p A238972 b:= (n, i)-> `if`(n=0 or i=1, [[1$n]], [map(x->
%p A238972     [i, x[]], b(n-i, min(n-i, i)))[], b(n, i-1)[]]):
%p A238972 T:= n-> map(x-> ceil((p-> add(nops(factorset(d)), d=divisors
%p A238972     (p)))(mul(ithprime(i)^x[i], i=1..nops(x)))/2), b(n$2))[]:
%p A238972 seq(T(n), n=0..9);  # _Alois P. Heinz_, Mar 28 2020
%Y A238972 Cf. A238959 in canonical order.
%Y A238972 Cf. A063008, A238950, A238964, A238973.
%K A238972 nonn,tabf
%O A238972 0,4
%A A238972 _Sung-Hyuk Cha_, Mar 07 2014
%E A238972 Offset changed and terms a(50) and beyond from _Andrew Howroyd_, Mar 28 2020