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

0,3

Links

Table of n, a(n) for n=0..36.

Formula

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

Example

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.

Mathematica

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

Crossrefs

Cf. A092669, A092670, A212657, A272083.

Sequence in context: A107281 A006744 A054175 * A000073 A255069 A160254

Adjacent sequences: A305439 A305440 A305441 * A305443 A305444 A305445

Keyword

nonn

Author

Peter Kagey, Jun 01 2018

Extensions

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

Status

approved