A238953 The size of divisor lattice D(n) in graded (reflected or not) colexicographic order of exponents.

0, 1, 2, 4, 3, 7, 12, 4, 10, 12, 20, 32, 5, 13, 17, 28, 33, 52, 80, 6, 16, 22, 24, 36, 46, 54, 72, 84, 128, 192, 7, 19, 27, 31, 44, 59, 64, 75, 92, 116, 135, 176, 204, 304, 448, 8, 22, 32, 38, 40, 52, 72, 82, 96, 104, 112, 148, 160, 186, 216, 224, 280, 324, 416, 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(A036035(n,k)).

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, 24, 36, 46, 54, 72, 84, 128, 192;
  ...

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)), [Vecrev(p) | p<-partitions(n)])}
{ for(n=0, 6, print(Row(n))) } \\ Andrew Howroyd, Apr 25 2020

Crossrefs

Cf. A062799 in graded colexicographic order.

Cf. A036035, A238964.

Sequence in context: A166017 A257504 A207625 * A238964 A035507 A138612

Adjacent sequences: A238950 A238951 A238952 * A238954 A238955 A238956

Keyword

nonn,tabf

Author

Sung-Hyuk Cha, Mar 07 2014

Extensions

Offset changed and terms a(64) and beyond from Andrew Howroyd, Apr 25 2020

Status

approved