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A238961 The size (the number of arcs) in the transitive closure of divisor lattice in graded colexicographic order. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 16 07:19 EDT 2021. Contains 347469 sequences. (Running on oeis4.)