A238969 Degree of divisor lattice in divisor lattice in canonical order.

0, 1, 2, 2, 2, 3, 3, 2, 3, 4, 4, 4, 2, 3, 4, 4, 5, 5, 5, 2, 3, 4, 4, 4, 5, 5, 6, 6, 6, 6, 2, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 7, 2, 3, 4, 4, 4, 5, 5, 4, 5, 6, 6, 6, 6, 6, 7, 7, 7, 8, 8, 8, 8, 8, 2, 3, 4, 4, 4, 5, 5, 4, 5, 6, 6, 6, 5, 6, 6, 7, 7, 7, 6, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 9

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) = A238949(A063008(n,k)). - Andrew Howroyd, Mar 26 2020

Example

Triangle T(n,k) begins:
  0;
  1;
  2, 2;
  2, 3, 3;
  2, 3, 4, 4, 4;
  2, 3, 4, 4, 5, 5, 5;
  2, 3, 4, 4, 4, 5, 5, 6, 6, 6, 6;
  ...

Prog

(PARI)
C(sig)={sum(i=1, #sig, if(sig[i]>1, 2, 1))}
Row(n)={apply(C, vecsort([Vecrev(p) | p<-partitions(n)], , 4))}
{ for(n=0, 8, print(Row(n))) } \\ Andrew Howroyd, Mar 26 2020

Crossrefs

Cf. A238956 in canonical order.

Cf. A063008, A238949.

Sequence in context: A077774 A344150 A128219 * A238956 A331415 A295511

Adjacent sequences: A238966 A238967 A238968 * A238970 A238971 A238972

Keyword

nonn,tabf

Author

Sung-Hyuk Cha, Mar 07 2014

Extensions

Offset changed and terms a(50) and beyond from Andrew Howroyd, Mar 26 2020

Status

approved