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A305442 Number of subsets of {1, 2, ..., n} such that the sum of the reciprocals is strictly less than 1. 0
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 24 21:09 EDT 2021. Contains 345425 sequences. (Running on oeis4.)