cp's OEIS Frontend

A238961 The size (the number of arcs) in the transitive closure of divisor lattice in graded colexicographic order.

%I A238961 #18 Apr 25 2020 18:19:24
%S A238961 0,1,3,5,6,12,19,10,22,27,42,65,15,35,48,74,90,138,211,21,51,75,84,
%T A238961 115,156,189,238,288,438,665,28,70,108,130,165,240,268,324,365,492,
%U A238961 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
%N A238961 The size (the number of arcs) in the transitive closure of divisor lattice in graded colexicographic order.
%H A238961 Andrew Howroyd, <a href="/A238961/b238961.txt">Table of n, a(n) for n = 0..2713</a> (rows 0..20)
%H A238961 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, Table A.1 entry |E^T(s)|.
%F A238961 T(n,k) = A238952(A036035(n,k)).
%e A238961 Triangle T(n,k) begins:
%e A238961    0;
%e A238961    1;
%e A238961    3,  5;
%e A238961    6, 12, 19;
%e A238961   10, 22, 27, 42,  65;
%e A238961   15, 35, 48, 74,  90, 138, 211;
%e A238961   21, 51, 75, 84, 115, 156, 189, 238, 288, 438, 665;
%e A238961   ...
%o A238961 (PARI) \\ here b(n) is A238952.
%o A238961 b(n) = {sumdivmult(n, d, numdiv(d)) - numdiv(n)}
%o A238961 N(sig)={prod(k=1, #sig, prime(k)^sig[k])}
%o A238961 Row(n)={apply(s->b(N(s)), [Vecrev(p) | p<-partitions(n)])}
%o A238961 { for(n=0, 6, print(Row(n))) } \\ _Andrew Howroyd_, Apr 25 2020
%Y A238961 Cf. A238952 in graded colexicographic order.
%Y A238961 Cf. A036035, A238974.
%K A238961 nonn,tabf
%O A238961 0,3
%A A238961 _Sung-Hyuk Cha_, Mar 07 2014
%E A238961 Offset changed and terms a(50) and beyond from _Andrew Howroyd_, Apr 25 2020