

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
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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

SungHyuk Cha, Mar 07 2014


EXTENSIONS

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


STATUS

approved



