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

%I A305442 #11 Jun 01 2018 18:16:44
%S A305442 1,1,2,4,7,13,24,44,81,149,274,501,918,1686,3110,5724,10543,19435,
%T A305442 35857,66198,122294,226135,418351,774372,1434089,2657205,4925796,
%U A305442 9135403,16949546,31460330,58415177,108502732,201603881,374707879,696649896,1295562234,2410000999
%N A305442 Number of subsets of {1, 2, ..., n} such that the sum of the reciprocals is strictly less than 1.
%F A305442 a(n) = A212657(n) - A092670(n).
%e A305442 For n = 4 the a(4) = 7 subsets are:
%e A305442 {}     because 0 < 1,
%e A305442 {2}    because 1/2 < 1,
%e A305442 {2, 3} because 1/2 + 1/3 = 5/6 < 1,
%e A305442 {2, 4} because 1/2 + 1/4 = 3/4 < 1,
%e A305442 {3}    because 1/3 < 1,
%e A305442 {3, 4} because 1/3 + 1/4 = 7/12 < 1, and
%e A305442 {4}    because 1/4 < 1.
%t A305442 a[n_] := 1 + Length@ Select[Subsets[Range[2,n], {1, n-1}], Total[1/#] < 1  &]; Array[a, 15] (* _Giovanni Resta_, Jun 01 2018 *)
%Y A305442 Cf. A092669, A092670, A212657, A272083.
%K A305442 nonn
%O A305442 0,3
%A A305442 _Peter Kagey_, Jun 01 2018
%E A305442 a(26)-a(36) from _Giovanni Resta_, Jun 01 2018