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

0,4

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

Example

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;
  ...

Prog

(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

Crossrefs

Cf. A238955 in canonical order.

Cf. A063008, A238946.

Sequence in context: A144867 A081520 A238955 * A217891 A322044 A010251

Adjacent sequences: A238965 A238966 A238967 * A238969 A238970 A238971

Keyword

nonn,tabf

Author

Sung-Hyuk Cha, Mar 07 2014

Extensions

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

Status

approved