A238968 - OEIS

%I #14 Mar 28 2020 19:21:38

%S 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 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 31,47,23,36,43,66,100,52,80,122,185,280

%N Maximal level size of arcs in divisor lattice in canonical order.

%H Andrew Howroyd, <a href="/A238968/b238968.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) = A238946(A063008(n,k)). - _Andrew Howroyd_, Mar 28 2020

%e Triangle T(n,k) begins:

%e   0;

%e   1;

%e   1, 2;

%e   1, 3, 6;

%e   1, 3, 4, 7, 12;

%e   1, 3, 5, 8, 11, 18, 30;

%e   1, 3, 5, 8,  6, 12, 19, 15, 24, 38, 60;

%e   ...

%o (PARI) \\ here b(n) is A238946.

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

%o Row(n)={apply(s->b(N(s)), vecsort([Vecrev(p) | p<-partitions(n)], , 4))}

%o { for(n=0, 8, print(Row(n))) } \\ _Andrew Howroyd_, Mar 28 2020

%Y Cf. A238955 in canonical order.

%Y Cf. A063008, A238946.

%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_, Mar 28 2020