A238961 The size (the number of arcs) in the transitive closure of divisor lattice in graded colexicographic order.
0, 1, 3, 5, 6, 12, 19, 10, 22, 27, 42, 65, 15, 35, 48, 74, 90, 138, 211, 21, 51, 75, 84, 115, 156, 189, 238, 288, 438, 665, 28, 70, 108, 130, 165, 240, 268, 324, 365, 492, 594, 746, 900, 1362, 2059, 36, 92, 147, 186, 200, 224, 342, 410, 495, 552, 519, 750, 836, 1008, 1215, 1135, 1524, 1836, 2302, 2772, 4182, 6305
Offset: 0
Examples
Triangle T(n,k) begins: 0; 1; 3, 5; 6, 12, 19; 10, 22, 27, 42, 65; 15, 35, 48, 74, 90, 138, 211; 21, 51, 75, 84, 115, 156, 189, 238, 288, 438, 665; ...
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, Table A.1 entry |E^T(s)|.
Programs
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PARI
\\ here b(n) is A238952. b(n) = {sumdivmult(n, d, numdiv(d)) - numdiv(n)} N(sig)={prod(k=1, #sig, prime(k)^sig[k])} Row(n)={apply(s->b(N(s)), [Vecrev(p) | p<-partitions(n)])} { for(n=0, 6, print(Row(n))) } \\ Andrew Howroyd, Apr 25 2020
Extensions
Offset changed and terms a(50) and beyond from Andrew Howroyd, Apr 25 2020