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A238974 The size (the number of arcs) in the transitive closure of divisor lattice in canonical order. 2
0, 1, 3, 5, 6, 12, 19, 10, 22, 27, 42, 65, 15, 35, 48, 74, 90, 138, 211, 21, 51, 75, 115, 84, 156, 238, 189, 288, 438, 665, 28, 70, 108, 165, 130, 240, 365, 268, 324, 492, 746, 594, 900, 1362, 2059, 36, 92, 147, 224, 186, 342, 519, 200, 410, 495, 750, 1135, 552, 836, 1008, 1524, 2302, 1215, 1836, 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.

FORMULA

T(n,k) = A238952(A063008(n,k)). - Andrew Howroyd, Mar 26 2020

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, 115, 84, 156, 238, 189, 288, 438, 665;

  ...

MAPLE

with(numtheory):

f:= n-> add(tau(d), d=divisors(n) minus {n}):

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-> f(mul(ithprime(i)^x[i], i=1..nops(x))), b(n$2))[]:

seq(T(n), n=0..9);  # Alois P. Heinz, Mar 26 2020

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)), vecsort([Vecrev(p) | p<-partitions(n)], , 4))}

{ for(n=0, 8, print(Row(n))) } \\ Andrew Howroyd, Mar 26 2020

CROSSREFS

Cf. A238961 in canonical order.

Cf. A063008, A238952.

Sequence in context: A086187 A088082 A238961 * A139013 A108337 A285534

Adjacent sequences:  A238971 A238972 A238973 * A238975 A238976 A238977

KEYWORD

nonn,tabf

AUTHOR

Sung-Hyuk Cha, Mar 07 2014

EXTENSIONS

Offset changed and terms a(50) and beyond from Andrew Howroyd, Mar 26 2020

STATUS

approved

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Last modified July 29 06:36 EDT 2021. Contains 346340 sequences. (Running on oeis4.)