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A238968 Maximal level size of arcs in divisor lattice in canonical order.

%I A238968 #14 Mar 28 2020 19:21:38
%S A238968 0,1,1,2,1,3,6,1,3,4,7,12,1,3,5,8,11,18,30,1,3,5,8,6,12,19,15,24,38,
%T A238968 60,1,3,5,8,7,13,20,16,19,30,46,37,58,90,140,1,3,5,8,7,13,20,8,17,20,
%U A238968 31,47,23,36,43,66,100,52,80,122,185,280
%N A238968 Maximal level size of arcs in divisor lattice in canonical order.
%H A238968 Andrew Howroyd, <a href="/A238968/b238968.txt">Table of n, a(n) for n = 0..2713</a> (rows 0..20)
%H A238968 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 A238968 T(n,k) = A238946(A063008(n,k)). - _Andrew Howroyd_, Mar 28 2020
%e A238968 Triangle T(n,k) begins:
%e A238968   0;
%e A238968   1;
%e A238968   1, 2;
%e A238968   1, 3, 6;
%e A238968   1, 3, 4, 7, 12;
%e A238968   1, 3, 5, 8, 11, 18, 30;
%e A238968   1, 3, 5, 8,  6, 12, 19, 15, 24, 38, 60;
%e A238968   ...
%o A238968 (PARI) \\ here b(n) is A238946.
%o A238968 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 A238968 N(sig)={prod(k=1, #sig, prime(k)^sig[k])}
%o A238968 Row(n)={apply(s->b(N(s)), vecsort([Vecrev(p) | p<-partitions(n)], , 4))}
%o A238968 { for(n=0, 8, print(Row(n))) } \\ _Andrew Howroyd_, Mar 28 2020
%Y A238968 Cf. A238955 in canonical order.
%Y A238968 Cf. A063008, A238946.
%K A238968 nonn,tabf
%O A238968 0,4
%A A238968 _Sung-Hyuk Cha_, Mar 07 2014
%E A238968 Offset changed and terms a(50) and beyond from _Andrew Howroyd_, Mar 28 2020