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A238971
The number of nodes at odd level in divisor lattice in canonical order.
3
0, 1, 1, 2, 2, 3, 4, 2, 4, 4, 6, 8, 3, 5, 6, 8, 9, 12, 16, 3, 6, 7, 10, 8, 12, 16, 13, 18, 24, 32, 4, 7, 9, 12, 10, 15, 20, 16, 18, 24, 32, 27, 36, 48, 64, 4, 8, 10, 14, 12, 18, 24, 12, 20, 22, 30, 40, 24, 32, 36, 48, 64, 40, 54, 72, 96, 128
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 25 2020: (Start)
T(n,k) = A056924(A063008(n,k)).
T(n,k) = A238963(n,k) - A238970(n,k).
T(n,k) = floor(A238963(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, 10, 8, 12, 16, 13, 18, 24, 32;
...
MAPLE
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-> floor(numtheory[tau](mul(ithprime(i)
^x[i], i=1..nops(x)))/2), b(n$2))[]:
seq(T(n), n=0..9); # Alois P. Heinz, Mar 25 2020
PROG
(PARI)
b(n)={numdiv(n)\2}
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 25 2020
CROSSREFS
Cf. A238958 in canonical order.
Sequence in context: A114892 A285705 A238958 * A194331 A372606 A290600
KEYWORD
nonn,tabf
AUTHOR
Sung-Hyuk Cha, Mar 07 2014
EXTENSIONS
Offset changed and terms a(50) and beyond from Andrew Howroyd, Mar 25 2020
STATUS
approved