A238968 Maximal level size of arcs in divisor lattice in canonical order.

0, 1, 1, 2, 1, 3, 6, 1, 3, 4, 7, 12, 1, 3, 5, 8, 11, 18, 30, 1, 3, 5, 8, 6, 12, 19, 15, 24, 38, 60, 1, 3, 5, 8, 7, 13, 20, 16, 19, 30, 46, 37, 58, 90, 140, 1, 3, 5, 8, 7, 13, 20, 8, 17, 20, 31, 47, 23, 36, 43, 66, 100, 52, 80, 122, 185, 280

Offset: 0

Author

Sung-Hyuk Cha, Mar 07 2014

Keywords

• nonn
• tabf

Examples

			Triangle T(n,k) begins:
  0;
  1;
  1, 2;
  1, 3, 6;
  1, 3, 4, 7, 12;
  1, 3, 5, 8, 11, 18, 30;
  1, 3, 5, 8,  6, 12, 19, 15, 24, 38, 60;
  ...
		

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. A238955 in canonical order.

Cf. A063008, A238946.

Programs

PARI

\\ here b(n) is A238946.
b(n)={if(n==1, 0, my(v=vector(bigomega(n))); fordiv(n, d, if(d>1, v[bigomega(d)] += omega(d))); vecmax(v))}
N(sig)={prod(k=1, #sig, prime(k)^sig[k])}
Row(n)={apply(s->b(N(s)), vecsort([Vecrev(p) | p<-partitions(n)], , 4))}
{ for(n=0, 8, print(Row(n))) } \\ Andrew Howroyd, Mar 28 2020

Formula

T(n,k) = A238946(A063008(n,k)). - Andrew Howroyd, Mar 28 2020

Extensions

Offset changed and terms a(50) and beyond from Andrew Howroyd, Mar 28 2020