A238968 -id:A238968 - cp's OEIS frontend

A238946 Maximal level size of arcs in divisor lattice D(n).

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

Offset: 1

Sung-Hyuk Cha, Mar 07 2014

nonn

A divisor d of n has level given by bigomega(d) and in-degree given by omega(d). The number of arcs on a level is the sum of the in-degrees of all divisors on the level. - Andrew Howroyd, Mar 28 2020

Andrew Howroyd, Table of n, a(n) for n = 1..1000 (terms 1..200 from Sung-Hyuk Cha)
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.

Cf. A001221 (omega), A001222 (bigomega), A062799, A096825, A238955, A238968.

a(n)={if(n==1, 0, my(v=vector(bigomega(n))); fordiv(n, d, if(d>1, v[bigomega(d)] += omega(d))); vecmax(v))} \\ Andrew Howroyd, Mar 28 2020

a(1) corrected by Andrew Howroyd, Mar 28 2020

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

Original entry on oeis.org

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

Sung-Hyuk Cha, Mar 07 2014

			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;
  ...

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.

Cf. A238946 in graded colexicographic order.

Cf. A036035, A238968.

\\ 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

T(n,k) = A238946(A036035(n,k)).

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

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A238946 Maximal level size of arcs in divisor lattice D(n).

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