

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, n1}], 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



