A238969 Degree of divisor lattice in divisor lattice in canonical 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, 5, 6, 6, 6, 6, 2, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 7, 2, 3, 4, 4, 4, 5, 5, 4, 5, 6, 6, 6, 6, 6, 7, 7, 7, 8, 8, 8, 8, 8, 2, 3, 4, 4, 4, 5, 5, 4, 5, 6, 6, 6, 5, 6, 6, 7, 7, 7, 6, 7, 7, 8, 8, 8, 8, 9, 9, 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, 5, 6, 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, vecsort([Vecrev(p) | p<-partitions(n)], , 4))} { for(n=0, 8, print(Row(n))) } \\ Andrew Howroyd, Mar 26 2020
Formula
Extensions
Offset changed and terms a(50) and beyond from Andrew Howroyd, Mar 26 2020