A122977 Number of sublattices of the divisor lattice of divisors of n that include n.
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, 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, 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
Offset: 1
Examples
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}.
Programs
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Mathematica
okQ[dd_List] := AllTrue[Subsets[dd, {2}], MemberQ[dd, GCD @@ #] && MemberQ[dd, LCM @@ #]&]; a[n_] := Select[Rest @ Subsets[Divisors[n]], Last[#] == n && okQ[#]&] // Length; Table[a[n], {n, 1, 100}] (* Jean-François Alcover, Aug 18 2022 *)
Comments