A238964 Size of divisor lattice in canonical order.

0, 1, 2, 4, 3, 7, 12, 4, 10, 12, 20, 32, 5, 13, 17, 28, 33, 52, 80, 6, 16, 22, 36, 24, 46, 72, 54, 84, 128, 192, 7, 19, 27, 44, 31, 59, 92, 64, 75, 116, 176, 135, 204, 304, 448, 8, 22, 32, 52, 38, 72, 112, 40, 82, 96, 148, 224, 104, 160, 186, 280, 416, 216, 324, 480, 704, 1024

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) = A062799(A063008(n,k)). - Andrew Howroyd, Mar 24 2020

Example

Triangle T(n,k) begins:
  0;
  1;
  2,  4;
  3,  7, 12;
  4, 10, 12, 20, 32;
  5, 13, 17, 28, 33, 52, 80;
  6, 16, 22, 36, 24, 46, 72, 54, 84, 128, 192;
  ...

Maple

with(numtheory):
b:= (n, i)-> `if`(n=0 or i=1, [[1$n]], [map(x->
    [i, x[]], b(n-i, min(n-i, i)))[], b(n, i-1)[]]):
T:= n-> map(x-> (p-> add(nops(factorset(d)), d=divisors
    (p)))(mul(ithprime(i)^x[i], i=1..nops(x))), b(n$2))[]:
seq(T(n), n=0..9);  # Alois P. Heinz, Mar 24 2020

Prog

(PARI) \\ here b(n) is A062799.
b(n)={sumdiv(n, d, omega(d))}
N(sig)={prod(k=1, #sig, prime(k)^sig[k])}
Row(n)={apply(s->b(N(s)), vecsort([Vecrev(p) | p<-partitions(n)], , 4))}
{concat(vector(9, n, Row(n-1)))} \\ Andrew Howroyd, Mar 24 2020

Crossrefs

Cf. A238953 in canonical order.

Cf. A062799, A063008.

Sequence in context: A257504 A207625 A238953 * A035507 A138612 A246680

Adjacent sequences: A238961 A238962 A238963 * A238965 A238966 A238967

Keyword

nonn,tabf

Author

Sung-Hyuk Cha, Mar 07 2014

Extensions

Offset changed and terms a(50) and beyond from Andrew Howroyd, Mar 24 2020

Status

approved