A238958 - OEIS

%I #14 Apr 01 2020 20:15:32

%S 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,

%T 4,7,9,10,12,15,16,18,20,24,27,32,36,48,64,4,8,10,12,12,14,18,20,22,

%U 24,24,30,32,36,40,40,48,54,64,72,96,128

%N The number of nodes at odd level in divisor lattice in graded colexicographic order.

%H Andrew Howroyd, <a href="/A238958/b238958.txt">Table of n, a(n) for n = 0..2713</a> (rows 0..20)

%H S.-H. Cha, E. G. DuCasse, and L. V. Quintas, <a href="http://arxiv.org/abs/1405.5283">Graph Invariants Based on the Divides Relation and Ordered by Prime Signatures</a>, arxiv:1405.5283 [math.NT], 2014.

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

%F From _Andrew Howroyd_, Apr 01 2020: (Start)

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

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

%e Triangle T(n,k) begins:

%e   0;

%e   1;

%e   1, 2;

%e   2, 3, 4;

%e   2, 4, 4, 6,  8;

%e   3, 5, 6, 8,  9, 12, 16;

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

%e   ...

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

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

%o N(sig)={prod(k=1, #sig, prime(k)^sig[k])}

%o Row(n)={apply(s->b(N(s)), [Vecrev(p) | p<-partitions(n)])}

%o { for(n=0, 8, print(Row(n))) } \\ _Andrew Howroyd_, Apr 01 2020

%Y Cf. A056924 in graded colexicographic order.

%Y Cf. A036035, A074139, A238957, A238971.

%K nonn,tabf

%O 0,4

%A _Sung-Hyuk Cha_, Mar 07 2014

%E Offset changed and terms a(50) and beyond from _Andrew Howroyd_, Apr 01 2020