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A238955 Maximal level size of arcs in divisor lattice in graded colexicographic order.

%I A238955 #18 Apr 26 2020 17:46:17
%S A238955 0,1,1,2,1,3,6,1,3,4,7,12,1,3,5,8,11,18,30,1,3,5,6,8,12,15,19,24,38,
%T A238955 60,1,3,5,7,8,13,16,19,20,30,37,46,58,90,140,1,3,5,7,8,8,13,17,20,23,
%U A238955 20,31,36,43,52,47,66,80,100,122,185,280
%N A238955 Maximal level size of arcs in divisor lattice in graded colexicographic order.
%H A238955 Andrew Howroyd, <a href="/A238955/b238955.txt">Table of n, a(n) for n = 0..2713</a> (rows 0..20)
%H A238955 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 A238955 T(n,k) = A238946(A036035(n,k)).
%e A238955 Triangle T(n,k) begins:
%e A238955   0;
%e A238955   1;
%e A238955   1, 2;
%e A238955   1, 3, ;
%e A238955   1, 3, 4, 7, 12;
%e A238955   1, 3, 5, 8, 11, 18, 30;
%e A238955   1, 3, 5, 6,  8, 12, 15, 19, 24, 38, 60;
%e A238955   ...
%o A238955 (PARI) \\ here b(n) is A238946.
%o A238955 b(n)={if(n==1, 0, my(v=vector(bigomega(n))); fordiv(n, d, if(d>1, v[bigomega(d)] += omega(d))); vecmax(v))}
%o A238955 N(sig)={prod(k=1, #sig, prime(k)^sig[k])}
%o A238955 Row(n)={apply(s->b(N(s)), [Vecrev(p) | p<-partitions(n)])}
%o A238955 { for(n=0, 6, print(Row(n))) } \\ _Andrew Howroyd_, Apr 25 2020
%Y A238955 Cf. A238946 in graded colexicographic order.
%Y A238955 Cf. A036035, A238968.
%K A238955 nonn,tabf
%O A238955 0,4
%A A238955 _Sung-Hyuk Cha_, Mar 07 2014
%E A238955 Offset changed and terms a(50) and beyond from _Andrew Howroyd_, Apr 25 2020