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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

%I

%S 1,1,2,4,7,13,24,44,81,149,274,501,918,1686,3110,5724,10543,19435,

%T 35857,66198,122294,226135,418351,774372,1434089,2657205,4925796,

%U 9135403,16949546,31460330,58415177,108502732,201603881,374707879,696649896,1295562234,2410000999

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

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

%e For n = 4 the a(4) = 7 subsets are:

%e {} because 0 < 1,

%e {2} because 1/2 < 1,

%e {2, 3} because 1/2 + 1/3 = 5/6 < 1,

%e {2, 4} because 1/2 + 1/4 = 3/4 < 1,

%e {3} because 1/3 < 1,

%e {3, 4} because 1/3 + 1/4 = 7/12 < 1, and

%e {4} because 1/4 < 1.

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

%Y Cf. A092669, A092670, A212657, A272083.

%K nonn

%O 0,3

%A _Peter Kagey_, Jun 01 2018

%E a(26)-a(36) from _Giovanni Resta_, Jun 01 2018

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Last modified August 4 00:29 EDT 2021. Contains 346441 sequences. (Running on oeis4.)