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A238953 The size of divisor lattice D(n) in graded (reflected or not) colexicographic order of exponents.

%I A238953 #21 Apr 25 2020 18:12:40
%S A238953 0,1,2,4,3,7,12,4,10,12,20,32,5,13,17,28,33,52,80,6,16,22,24,36,46,54,
%T A238953 72,84,128,192,7,19,27,31,44,59,64,75,92,116,135,176,204,304,448,8,22,
%U A238953 32,38,40,52,72,82,96,104,112,148,160,186,216,224,280,324,416,480,704,1024
%N A238953 The size of divisor lattice D(n) in graded (reflected or not) colexicographic order of exponents.
%H A238953 Andrew Howroyd, <a href="/A238953/b238953.txt">Table of n, a(n) for n = 0..2713</a> (rows 0..20)
%H A238953 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 A238953 T(n,k) = A062799(A036035(n,k)).
%e A238953 Triangle T(n,k) begins:
%e A238953   0;
%e A238953   1;
%e A238953   2,  4;
%e A238953   3,  7, 12;
%e A238953   4, 10, 12, 20, 32;
%e A238953   5, 13, 17, 28, 33, 52, 80;
%e A238953   6, 16, 22, 24, 36, 46, 54, 72, 84, 128, 192;
%e A238953   ...
%o A238953 (PARI) \\ here b(n) is A062799.
%o A238953 b(n)={sumdiv(n, d, omega(d))}
%o A238953 N(sig)={prod(k=1, #sig, prime(k)^sig[k])}
%o A238953 Row(n)={apply(s->b(N(s)), [Vecrev(p) | p<-partitions(n)])}
%o A238953 { for(n=0, 6, print(Row(n))) } \\ _Andrew Howroyd_, Apr 25 2020
%Y A238953 Cf. A062799 in graded colexicographic order.
%Y A238953 Cf. A036035, A238964.
%K A238953 nonn,tabf
%O A238953 0,3
%A A238953 _Sung-Hyuk Cha_, Mar 07 2014
%E A238953 Offset changed and terms a(64) and beyond from _Andrew Howroyd_, Apr 25 2020