A238951 -id:A238951 - cp's OEIS frontend

A238950 Number of arcs from even to odd level vertices in divisor lattice D(n).

0, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 4, 1, 2, 2, 2, 1, 4, 1, 4, 2, 2, 1, 5, 1, 2, 2, 4, 1, 6, 1, 3, 2, 2, 2, 6, 1, 2, 2, 5, 1, 6, 1, 4, 4, 2, 1, 7, 1, 4, 2, 4, 1, 5, 2, 5, 2, 2, 1, 10, 1, 2, 4, 3, 2, 6, 1, 4, 2, 6, 1, 9, 1, 2, 4, 4, 2, 6, 1, 7, 2, 2, 1, 10, 2, 2

Offset: 1

Sung-Hyuk Cha, Mar 07 2014

nonn

R. J. Mathar, Table of n, a(n) for n = 1..1000
Sung-Hyuk 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 (see 11th line in Table 1).

Cf. A062799, A038548, A358769.

read("transforms") :
omega := [seq(A001221(n), n=1..1000)] :
ones := [seq(1,n=1..1000)] :
a062799 := DIRICHLET(ones,omega) ;
for n from 1 do
    a238951 := floor(op(n,a062799)/2) ;
    a238950 := op(n,a062799)-floor(op(n,a062799)/2) ;
    printf("%d %d\n",n,a238950) ;
end do: # R. J. Mathar, May 28 2017

a(n) = A062799(n) - A238951(n). - Eq. (2.37) [Cha] - R. J. Mathar, May 27 2017

a(n) = (A062799(n) + A358769(n))/2. - Ridouane Oudra, May 16 2025

A238960 The number of arcs from odd to even level vertices in divisor lattice in graded colexicographic order.

Original entry on oeis.org

0, 0, 1, 2, 1, 3, 6, 2, 5, 6, 10, 16, 2, 6, 8, 14, 16, 26, 40, 3, 8, 11, 12, 18, 23, 27, 36, 42, 64, 96, 3, 9, 13, 15, 22, 29, 32, 37, 46, 58, 67, 88, 102, 152, 224, 4, 11, 16, 19, 20, 26, 36, 41, 48, 52, 56, 74, 80, 93, 108, 112, 140, 162, 208, 240, 352, 512

Offset: 0

Sung-Hyuk Cha, Mar 07 2014

			Triangle T(n,k) begins:
  0;
  0;
  1, 2;
  1, 3,  6;
  2, 5,  6, 10, 16;
  2, 6,  8, 14, 16, 26, 40;
  3, 8, 11, 12, 18, 23, 27, 36, 42, 64, 96;
  ...

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_O(S)|.

Cf. A238951 in graded colexicographic order.

Cf. A036035, A238953, A238959, A238973.

T(n,k) = A238951(A036035(n,k)).
From Andrew Howroyd, Apr 25 2020: (Start)
T(n,k) = floor(A238953(n,k)/2).
T(n,k) = A238953(n,k) - A238959(n,k). (End)

Offset changed and terms a(50) and beyond from Andrew Howroyd, Apr 25 2020

A238973 The number of arcs from odd to even level vertices in divisor lattice in canonical order.

Original entry on oeis.org

0, 0, 1, 2, 1, 3, 6, 2, 5, 6, 10, 16, 2, 6, 8, 14, 16, 26, 40, 3, 8, 11, 18, 12, 23, 36, 27, 42, 64, 96, 3, 9, 13, 22, 15, 29, 46, 32, 37, 58, 88, 67, 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

Offset: 0

Sung-Hyuk Cha, Mar 07 2014

			Triangle T(n,k) begins:
  0;
  0;
  1, 2;
  1, 3,  6;
  2, 5,  6, 10, 16;
  2, 6,  8, 14, 16, 26, 40;
  3, 8, 11, 18, 12, 23, 36, 27, 42, 64, 96;
  ...

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.

Cf. A238960 in canonical order.

Cf. A063008, A238951, A238964, A238972.

From Andrew Howroyd, Mar 28 2020: (Start)
T(n,k) = A238951(A063008(n,k)).
T(n,k) = A238964(n,k) - A238972(n,k).
T(n,k) = floor(A238964(n,k)/2). (End)

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

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A238950 Number of arcs from even to odd level vertices in divisor lattice D(n).

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A238960 The number of arcs from odd to even level vertices in divisor lattice in graded colexicographic order.

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A238973 The number of arcs from odd to even level vertices in divisor lattice in canonical order.

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