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A238957 The number of nodes at even level in divisor lattice in graded colexicographic order.

%I A238957 #18 Apr 01 2020 20:14:30
%S A238957 1,1,2,2,2,3,4,3,4,5,6,8,3,5,6,8,9,12,16,4,6,8,8,10,12,14,16,18,24,32,
%T A238957 4,7,9,10,12,15,16,18,20,24,27,32,36,48,64,5,8,11,12,13,14,18,20,23,
%U A238957 24,24,30,32,36,41,40,48,54,64,72,96,128
%N A238957 The number of nodes at even level in divisor lattice in graded colexicographic order.
%H A238957 Andrew Howroyd, <a href="/A238957/b238957.txt">Table of n, a(n) for n = 0..2713</a> (rows 0..20)
%H A238957 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 A238957 T(n,k) = A038548(A036035(n,k)).
%F A238957 From _Andrew Howroyd_, Apr 01 2020: (Start)
%F A238957 T(n,k) = A074139(n,k) - A238958(n,k).
%F A238957 T(n,k) = ceiling(A074139(n,k)/2). (End)
%e A238957 Triangle T(n,k) begins:
%e A238957   1;
%e A238957   1;
%e A238957   2, 2;
%e A238957   2, 3, 4;
%e A238957   3, 4, 5, 6,  8;
%e A238957   3, 5, 6, 8,  9, 12, 16;
%e A238957   4, 6, 8, 8, 10, 12, 14, 16, 18, 24, 32;
%e A238957   ...
%o A238957 (PARI) \\ here b(n) is A038548.
%o A238957 b(n)={ceil(numdiv(n)/2)}
%o A238957 N(sig)={prod(k=1, #sig, prime(k)^sig[k])}
%o A238957 Row(n)={apply(s->b(N(s)), [Vecrev(p) | p<-partitions(n)])}
%o A238957 { for(n=0, 8, print(Row(n))) } \\ _Andrew Howroyd_, Apr 01 2020
%Y A238957 Cf. A038548 in graded colexicographic order.
%Y A238957 Cf. A036035, A074139, A238958, A238970.
%K A238957 nonn,tabf
%O A238957 0,3
%A A238957 _Sung-Hyuk Cha_, Mar 07 2014
%E A238957 Offset changed and terms a(50) and beyond from _Andrew Howroyd_, Apr 01 2020