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A238954 Maximal size of an antichain in graded colexicographic order of exponents.

%I A238954 #17 Apr 26 2020 17:41:40
%S A238954 1,1,1,2,1,2,3,1,2,3,4,6,1,2,3,4,5,7,10,1,2,3,4,4,6,7,8,10,14,20,1,2,
%T A238954 3,4,4,6,7,8,8,11,13,15,18,25,35,1,2,3,4,5,4,6,8,9,10,8,12,14,16,19,
%U A238954 16,22,26,30,36,50,70,1,2,3,4,5,4,6,8,9,9,11,12,8,12,15,17,19,22,16,23,26,30,35,31,41,48,56,66,91,126
%N A238954 Maximal size of an antichain in graded colexicographic order of exponents.
%H A238954 Andrew Howroyd, <a href="/A238954/b238954.txt">Table of n, a(n) for n = 0..2713</a> (rows 0..20)
%H A238954 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 A238954 T(n,k) = A096825(A036035(n,k)).
%e A238954 Triangle T(n,k) begins:
%e A238954   1;
%e A238954   1;
%e A238954   1, 2;
%e A238954   1, 2, 3;
%e A238954   1, 2, 3, 4, 6;
%e A238954   1, 2, 3, 4, 5, 7, 10;
%e A238954   1, 2, 3, 4, 4, 6,  7, 8, 10, 14, 20;
%e A238954   ...
%o A238954 (PARI) \\ here b(n) is A096825.
%o A238954 b(n)={my(h=bigomega(n)\2); sumdiv(n, d, bigomega(d)==h)}
%o A238954 N(sig)={prod(k=1, #sig, prime(k)^sig[k])}
%o A238954 Row(n)={apply(s->b(N(s)), [Vecrev(p) | p<-partitions(n)])}
%o A238954 { for(n=0, 6, print(Row(n))) } \\ _Andrew Howroyd_, Apr 25 2020
%Y A238954 Cf. A096825 in graded colexicographic order.
%Y A238954 Cf. A036035, A238967.
%K A238954 nonn,tabf
%O A238954 0,4
%A A238954 _Sung-Hyuk Cha_, Mar 07 2014
%E A238954 Offset changed and terms a(50) and beyond from _Andrew Howroyd_, Apr 25 2020