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A238958 The number of nodes at odd level in divisor lattice in graded colexicographic order. 3
0, 1, 1, 2, 2, 3, 4, 2, 4, 4, 6, 8, 3, 5, 6, 8, 9, 12, 16, 3, 6, 7, 8, 10, 12, 13, 16, 18, 24, 32, 4, 7, 9, 10, 12, 15, 16, 18, 20, 24, 27, 32, 36, 48, 64, 4, 8, 10, 12, 12, 14, 18, 20, 22, 24, 24, 30, 32, 36, 40, 40, 48, 54, 64, 72, 96, 128 (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

T(n,k) = A056924(A036035(n,k)).

From Andrew Howroyd, Apr 01 2020: (Start)

T(n,k) = A074139(n,k) - A238957(n,k).

T(n,k) = floor(A074139(n,k)/2). (End)

EXAMPLE

Triangle T(n,k) begins:

  0;

  1;

  1, 2;

  2, 3, 4;

  2, 4, 4, 6,  8;

  3, 5, 6, 8,  9, 12, 16;

  3, 6, 7, 8, 10, 12, 13, 16, 18, 24, 32;

  ...

PROG

(PARI) \\ here b(n) is A056924.

b(n)={numdiv(n)\2}

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, 8, print(Row(n))) } \\ Andrew Howroyd, Apr 01 2020

CROSSREFS

Cf. A056924 in graded colexicographic order.

Cf. A036035, A074139, A238957, A238971.

Sequence in context: A098223 A114892 A285705 * A238971 A194331 A290600

Adjacent sequences:  A238955 A238956 A238957 * A238959 A238960 A238961

KEYWORD

nonn,tabf

AUTHOR

Sung-Hyuk Cha, Mar 07 2014

EXTENSIONS

Offset changed and terms a(50) and beyond from Andrew Howroyd, Apr 01 2020

STATUS

approved

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Last modified June 24 11:01 EDT 2021. Contains 345416 sequences. (Running on oeis4.)