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

0,4

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.

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)

Example

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;
  ...

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

Crossrefs

Cf. A238959 in canonical order.

Cf. A063008, A238950, A238964, A238973.

Sequence in context: A278217 A191674 A238959 * A207193 A319579 A286631

Adjacent sequences: A238969 A238970 A238971 * A238973 A238974 A238975

Keyword

nonn,tabf

Author

Sung-Hyuk Cha, Mar 07 2014

Extensions

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

Status

approved