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A238972 The number of arcs from even to odd level vertices in divisor lattice in canonical order. 3
0, 1, 1, 2, 2, 4, 6, 2, 5, 6, 10, 16, 3, 7, 9, 14, 17, 26, 40, 3, 8, 11, 18, 12, 23, 36, 27, 42, 64, 96, 4, 10, 14, 22, 16, 30, 46, 32, 38, 58, 88, 68, 102, 152, 224, 4, 11, 16, 26, 19, 36, 56, 20, 41, 48, 74, 112, 52, 80, 93, 140, 208, 108, 162, 240, 352, 512 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

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

From Andrew Howroyd, Mar 28 2020: (Start)

T(n,k) = A238950(A063008(n,k)).

T(n,k) = A238964(n,k) - A238973(n,k).

T(n,k) = ceiling(A238964(n,k)/2). (End)

EXAMPLE

Triangle T(n,k) begins:

  0;

  1;

  1, 2;

  2, 4,  6;

  2, 5,  6, 10, 16;

  3, 7,  9, 14, 17, 26, 40;

  3, 8, 11, 18, 12, 23, 36, 27, 42, 64, 96;

  ...

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-> ceil((p-> add(nops(factorset(d)), d=divisors

    (p)))(mul(ithprime(i)^x[i], i=1..nops(x)))/2), b(n$2))[]:

seq(T(n), n=0..9);  # Alois P. Heinz, Mar 28 2020

CROSSREFS

Cf. A238959 in canonical order.

Cf. A063008, A238950, A238964, A238973.

Sequence in context: A278217 A191674 A238959 * A207193 A319579 A286631

Adjacent sequences:  A238969 A238970 A238971 * A238973 A238974 A238975

KEYWORD

nonn,tabf

AUTHOR

Sung-Hyuk Cha, Mar 07 2014

EXTENSIONS

Offset changed and terms a(50) and beyond from Andrew Howroyd, Mar 28 2020

STATUS

approved

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Last modified July 28 00:54 EDT 2021. Contains 346316 sequences. (Running on oeis4.)