A238954 Maximal size of an antichain in graded colexicographic order of exponents.

1, 1, 1, 2, 1, 2, 3, 1, 2, 3, 4, 6, 1, 2, 3, 4, 5, 7, 10, 1, 2, 3, 4, 4, 6, 7, 8, 10, 14, 20, 1, 2, 3, 4, 4, 6, 7, 8, 8, 11, 13, 15, 18, 25, 35, 1, 2, 3, 4, 5, 4, 6, 8, 9, 10, 8, 12, 14, 16, 19, 16, 22, 26, 30, 36, 50, 70, 1, 2, 3, 4, 5, 4, 6, 8, 9, 9, 11, 12, 8, 12, 15, 17, 19, 22, 16, 23, 26, 30, 35, 31, 41, 48, 56, 66, 91, 126

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) = A096825(A036035(n,k)).

Example

Triangle T(n,k) begins:
  1;
  1;
  1, 2;
  1, 2, 3;
  1, 2, 3, 4, 6;
  1, 2, 3, 4, 5, 7, 10;
  1, 2, 3, 4, 4, 6,  7, 8, 10, 14, 20;
  ...

Prog

(PARI) \\ here b(n) is A096825.
b(n)={my(h=bigomega(n)\2); sumdiv(n, d, bigomega(d)==h)}
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, 6, print(Row(n))) } \\ Andrew Howroyd, Apr 25 2020

Crossrefs

Cf. A096825 in graded colexicographic order.

Cf. A036035, A238967.

Sequence in context: A162192 A329795 A329794 * A238967 A066657 A119444

Adjacent sequences: A238951 A238952 A238953 * A238955 A238956 A238957

Keyword

nonn,tabf

Author

Sung-Hyuk Cha, Mar 07 2014

Extensions

Offset changed and terms a(50) and beyond from Andrew Howroyd, Apr 25 2020

Status

approved