A238958 The number of nodes at odd level in divisor lattice in graded colexicographic order.

0, 1, 1, 2, 2, 3, 4, 2, 4, 4, 6, 8, 3, 5, 6, 8, 9, 12, 16, 3, 6, 7, 8, 10, 12, 13, 16, 18, 24, 32, 4, 7, 9, 10, 12, 15, 16, 18, 20, 24, 27, 32, 36, 48, 64, 4, 8, 10, 12, 12, 14, 18, 20, 22, 24, 24, 30, 32, 36, 40, 40, 48, 54, 64, 72, 96, 128

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

T(n,k) = A056924(A036035(n,k)).

From Andrew Howroyd, Apr 01 2020: (Start)

T(n,k) = A074139(n,k) - A238957(n,k).

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

Example

Triangle T(n,k) begins:
  0;
  1;
  1, 2;
  2, 3, 4;
  2, 4, 4, 6,  8;
  3, 5, 6, 8,  9, 12, 16;
  3, 6, 7, 8, 10, 12, 13, 16, 18, 24, 32;
  ...

Prog

(PARI) \\ here b(n) is A056924.
b(n)={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. A056924 in graded colexicographic order.

Cf. A036035, A074139, A238957, A238971.

Sequence in context: A098223 A114892 A285705 * A238971 A194331 A372606

Adjacent sequences: A238955 A238956 A238957 * A238959 A238960 A238961

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