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

0,3

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

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)

Example

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;
  ...

Prog

(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

Crossrefs

Cf. A038548 in graded colexicographic order.

Cf. A036035, A074139, A238958, A238970.

Sequence in context: A362739 A112184 A112213 * A238970 A085755 A330216

Adjacent sequences: A238954 A238955 A238956 * A238958 A238959 A238960

Keyword

nonn,tabf

Author

Sung-Hyuk Cha, Mar 07 2014

Extensions

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

Status

approved