A238961 The size (the number of arcs) in the transitive closure of divisor lattice in graded colexicographic order.

0, 1, 3, 5, 6, 12, 19, 10, 22, 27, 42, 65, 15, 35, 48, 74, 90, 138, 211, 21, 51, 75, 84, 115, 156, 189, 238, 288, 438, 665, 28, 70, 108, 130, 165, 240, 268, 324, 365, 492, 594, 746, 900, 1362, 2059, 36, 92, 147, 186, 200, 224, 342, 410, 495, 552, 519, 750, 836, 1008, 1215, 1135, 1524, 1836, 2302, 2772, 4182, 6305

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, Table A.1 entry |E^T(s)|.

Formula

T(n,k) = A238952(A036035(n,k)).

Example

Triangle T(n,k) begins:
   0;
   1;
   3,  5;
   6, 12, 19;
  10, 22, 27, 42,  65;
  15, 35, 48, 74,  90, 138, 211;
  21, 51, 75, 84, 115, 156, 189, 238, 288, 438, 665;
  ...

Prog

(PARI) \\ here b(n) is A238952.
b(n) = {sumdivmult(n, d, numdiv(d)) - numdiv(n)}
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. A238952 in graded colexicographic order.

Cf. A036035, A238974.

Sequence in context: A100712 A086187 A088082 * A238974 A139013 A108337

Adjacent sequences: A238958 A238959 A238960 * A238962 A238963 A238964

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