cp's OEIS Frontend

A122977 Number of sublattices of the divisor lattice of divisors of n that include n.

%I A122977 #17 Aug 18 2022 08:28:12
%S A122977 1,2,2,4,2,7,2,8,4,7,2,21,2,7,7,16,2,21,2,21,7,7,2,58,4,7,8,21,2,45,2,
%T A122977 32,7,7,7,84,2,7,7,58,2,45,2,21,21,7,2,152,4,21,7,21,2,58,7,58,7,7,2,
%U A122977 200,2,7,21,64,7,45,2,21,7,45,2,293,2,7,21,21,7,45,2,152,16,7,2,200,7,7
%N A122977 Number of sublattices of the divisor lattice of divisors of n that include n.
%C A122977 A divisor lattice is closed under GCD and LCM. First differences of A074986. Depends only on the prime signature of n.
%F A122977 a(A002110(n)) = A326878(n). - _Andrew Howroyd_, Apr 17 2020
%e A122977 The a(6) = 7 sublattices of {1,2,3,6} that include 6 are: {6}, {1,6}, {2,6}, {3,6}, {1,2,6}, {1,3,6}, {1,2,3,6}.
%t A122977 okQ[dd_List] := AllTrue[Subsets[dd, {2}], MemberQ[dd, GCD @@ #] && MemberQ[dd, LCM @@ #]&];
%t A122977 a[n_] := Select[Rest @ Subsets[Divisors[n]], Last[#] == n && okQ[#]&] // Length;
%t A122977 Table[a[n], {n, 1, 100}] (* _Jean-François Alcover_, Aug 18 2022 *)
%Y A122977 Cf. A051839, A074986, A122978, A122979, A122980, A326878.
%K A122977 nonn,nice
%O A122977 1,2
%A A122977 _Franklin T. Adams-Watters_, Sep 21 2006