A238956 Degree of divisor lattice in graded colexicographic order.
0, 1, 2, 2, 2, 3, 3, 2, 3, 4, 4, 4, 2, 3, 4, 4, 5, 5, 5, 2, 3, 4, 4, 4, 5, 6, 5, 6, 6, 6, 2, 3, 4, 4, 4, 5, 5, 6, 5, 6, 7, 6, 7, 7, 7, 2, 3, 4, 4, 4, 4, 5, 5, 6, 6, 5, 6, 6, 7, 8, 6, 7, 8, 7, 8, 8, 8, 2, 3, 4, 4, 4, 4, 5, 5, 5, 6, 6, 6, 5, 6, 6, 7, 7, 8, 6, 7, 7, 8, 9, 7, 8, 9, 8, 9, 9, 9
Offset: 0
Examples
Triangle T(n,k) begins: 0; 1; 2, 2; 2, 3, 3; 2, 3, 4, 4, 4; 2, 3, 4, 4, 5, 5, 5; 2, 3, 4, 4, 4, 5, 6, 5, 6, 6, 6; ...
Links
- Andrew Howroyd, Table of n, a(n) for n = 0..2713 (rows 0..20)
- S.-H. Cha, E. G. DuCasse, and L. V. Quintas, Graph Invariants Based on the Divides Relation and Ordered by Prime Signatures, arxiv:1405.5283 [math.NT], 2014.
Programs
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PARI
C(sig)={sum(i=1, #sig, if(sig[i]>1, 2, 1))} Row(n)={apply(C, [Vecrev(p) | p<-partitions(n)])} { for(n=0, 8, print(Row(n))) } \\ Andrew Howroyd, Apr 01 2020
Extensions
Offset changed and terms a(50) and beyond from Andrew Howroyd, Apr 01 2020