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

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, 64, 96, 4, 10, 14, 22, 16, 30, 46, 32, 38, 58, 88, 68, 102, 152, 224, 4, 11, 16, 26, 19, 36, 56, 20, 41, 48, 74, 112, 52, 80, 93, 140, 208, 108, 162, 240, 352, 512

Offset: 0

Author

Sung-Hyuk Cha, Mar 07 2014

Keywords

• nonn
• tabf

Examples

			Triangle T(n,k) begins:
  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, 64, 96;
  ...
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..2713 (rows 0..20)
• 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. A238959 in canonical order.

Cf. A063008, A238950, A238964, A238973.

Programs

Maple

with(numtheory):
b:= (n, i)-> `if`(n=0 or i=1, [[1$n]], [map(x->
    [i, x[]], b(n-i, min(n-i, i)))[], b(n, i-1)[]]):
T:= n-> map(x-> ceil((p-> add(nops(factorset(d)), d=divisors
    (p)))(mul(ithprime(i)^x[i], i=1..nops(x)))/2), b(n$2))[]:
seq(T(n), n=0..9);  # Alois P. Heinz, Mar 28 2020

Formula

From Andrew Howroyd, Mar 28 2020: (Start)

T(n,k) = A238950(A063008(n,k)).

T(n,k) = A238964(n,k) - A238973(n,k).

T(n,k) = ceiling(A238964(n,k)/2). (End)

Extensions

Offset changed and terms a(50) and beyond from Andrew Howroyd, Mar 28 2020