A238955 Maximal level size of arcs in divisor lattice in graded colexicographic order.

0, 1, 1, 2, 1, 3, 6, 1, 3, 4, 7, 12, 1, 3, 5, 8, 11, 18, 30, 1, 3, 5, 6, 8, 12, 15, 19, 24, 38, 60, 1, 3, 5, 7, 8, 13, 16, 19, 20, 30, 37, 46, 58, 90, 140, 1, 3, 5, 7, 8, 8, 13, 17, 20, 23, 20, 31, 36, 43, 52, 47, 66, 80, 100, 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(A036035(n,k)).

Example

Triangle T(n,k) begins:
  0;
  1;
  1, 2;
  1, 3, ;
  1, 3, 4, 7, 12;
  1, 3, 5, 8, 11, 18, 30;
  1, 3, 5, 6,  8, 12, 15, 19, 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)), [Vecrev(p) | p<-partitions(n)])}
{ for(n=0, 6, print(Row(n))) } \\ Andrew Howroyd, Apr 25 2020

Crossrefs

Cf. A238946 in graded colexicographic order.

Cf. A036035, A238968.

Sequence in context: A077877 A144867 A081520 * A238968 A217891 A322044

Adjacent sequences: A238952 A238953 A238954 * A238956 A238957 A238958

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