A238957 The number of nodes at even level in divisor lattice in graded colexicographic order.

1, 1, 2, 2, 2, 3, 4, 3, 4, 5, 6, 8, 3, 5, 6, 8, 9, 12, 16, 4, 6, 8, 8, 10, 12, 14, 16, 18, 24, 32, 4, 7, 9, 10, 12, 15, 16, 18, 20, 24, 27, 32, 36, 48, 64, 5, 8, 11, 12, 13, 14, 18, 20, 23, 24, 24, 30, 32, 36, 41, 40, 48, 54, 64, 72, 96, 128

Offset: 0

Author

Sung-Hyuk Cha, Mar 07 2014

Keywords

• nonn
• tabf

Examples

			Triangle T(n,k) begins:
  1;
  1;
  2, 2;
  2, 3, 4;
  3, 4, 5, 6,  8;
  3, 5, 6, 8,  9, 12, 16;
  4, 6, 8, 8, 10, 12, 14, 16, 18, 24, 32;
  ...
		

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. A038548 in graded colexicographic order.

Cf. A036035, A074139, A238958, A238970.

Programs

PARI

\\ here b(n) is A038548.
b(n)={ceil(numdiv(n)/2)}
N(sig)={prod(k=1, #sig, prime(k)^sig[k])}
Row(n)={apply(s->b(N(s)), [Vecrev(p) | p<-partitions(n)])}
{ for(n=0, 8, print(Row(n))) } \\ Andrew Howroyd, Apr 01 2020

Formula

T(n,k) = A038548(A036035(n,k)).

From Andrew Howroyd, Apr 01 2020: (Start)

T(n,k) = A074139(n,k) - A238958(n,k).

T(n,k) = ceiling(A074139(n,k)/2). (End)

Extensions

Offset changed and terms a(50) and beyond from Andrew Howroyd, Apr 01 2020