A305442 Number of subsets of {1, 2, ..., n} such that the sum of the reciprocals is strictly less than 1.

1, 1, 2, 4, 7, 13, 24, 44, 81, 149, 274, 501, 918, 1686, 3110, 5724, 10543, 19435, 35857, 66198, 122294, 226135, 418351, 774372, 1434089, 2657205, 4925796, 9135403, 16949546, 31460330, 58415177, 108502732, 201603881, 374707879, 696649896, 1295562234, 2410000999

Offset: 0

Author

Peter Kagey, Jun 01 2018

Keywords

• nonn

Examples

			For n = 4 the a(4) = 7 subsets are:
{}     because 0 < 1,
{2}    because 1/2 < 1,
{2, 3} because 1/2 + 1/3 = 5/6 < 1,
{2, 4} because 1/2 + 1/4 = 3/4 < 1,
{3}    because 1/3 < 1,
{3, 4} because 1/3 + 1/4 = 7/12 < 1, and
{4}    because 1/4 < 1.
		

Crossrefs

Cf. A092669, A092670, A212657, A272083.

Programs

Mathematica

a[n_] := 1 + Length@ Select[Subsets[Range[2,n], {1, n-1}], Total[1/#] < 1  &]; Array[a, 15] (* Giovanni Resta, Jun 01 2018 *)

Formula

a(n) = A212657(n) - A092670(n).

Extensions

a(26)-a(36) from Giovanni Resta, Jun 01 2018