cp's OEIS Frontend

A337256 Number of strict chains of divisors of n.

%I A337256 #7 Aug 24 2020 01:03:21
%S A337256 2,4,4,8,4,12,4,16,8,12,4,32,4,12,12,32,4,32,4,32,12,12,4,80,8,12,16,
%T A337256 32,4,52,4,64,12,12,12,104,4,12,12,80,4,52,4,32,32,12,4,192,8,32,12,
%U A337256 32,4,80,12,80,12,12,4,176,4,12,32,128,12,52,4,32,12,52
%N A337256 Number of strict chains of divisors of n.
%F A337256 a(n) = A253249(n) + 1.
%e A337256 The a(n) chains for n = 1, 2, 4, 6, 8 (empty chains shown as 0):
%e A337256   0  0    0      0      0
%e A337256   1  1    1      1      1
%e A337256      2    2      2      2
%e A337256      2/1  4      3      4
%e A337256           2/1    6      8
%e A337256           4/1    2/1    2/1
%e A337256           4/2    3/1    4/1
%e A337256           4/2/1  6/1    4/2
%e A337256                  6/2    8/1
%e A337256                  6/3    8/2
%e A337256                  6/2/1  8/4
%e A337256                  6/3/1  4/2/1
%e A337256                         8/2/1
%e A337256                         8/4/1
%e A337256                         8/4/2
%e A337256                         8/4/2/1
%t A337256 stableSets[u_,Q_]:=If[Length[u]==0,{{}},With[{w=First[u]},Join[stableSets[DeleteCases[u,w],Q],Prepend[#,w]&/@stableSets[DeleteCases[u,r_/;r==w||Q[r,w]||Q[w,r]],Q]]]];
%t A337256 Table[Length[stableSets[Divisors[n],!(Divisible[#1,#2]||Divisible[#2,#1])&]],{n,10}]
%Y A337256 A067824 is the case of chains starting with n (or ending with 1).
%Y A337256 A074206 is the case of chains from n to 1.
%Y A337256 A253249 is the nonempty case.
%Y A337256 A000005 counts divisors.
%Y A337256 A001055 counts factorizations.
%Y A337256 A001222 counts prime factors with multiplicity.
%Y A337256 A074206 counts chains of divisors from n to 1.
%Y A337256 A122651 counts chains of divisors summing to n.
%Y A337256 A167865 counts chains of divisors > 1 summing to n.
%Y A337256 A334996 appears to count chains of divisors from n to 1 by length.
%Y A337256 A337070 counts chains of divisors starting with A006939(n).
%Y A337256 A337071 counts chains of divisors starting with n!.
%Y A337256 A337255 counts chains of divisors starting with n by length.
%Y A337256 Cf. A001221, A002033, A008480, A124010, A251683, A337105, A337107.
%K A337256 nonn
%O A337256 1,1
%A A337256 _Gus Wiseman_, Aug 23 2020