A212658
Number of multisets {1^k1, 2^k2, ..., n^kn}, ki >= 0, with the sum of reciprocals <= 1.
Original entry on oeis.org
1, 2, 4, 8, 17, 37, 86, 199, 475, 1138, 2769, 6748, 16613, 40904, 101317, 251401, 624958, 1555940, 3882708, 9701790, 24276866, 60817940, 152508653, 382828565, 961859364, 2418662434, 6086480305, 15327208770, 38622901484, 97384378728, 245686368946, 620158662562
Offset: 0
A305442
Number of subsets of {1, 2, ..., n} such that the sum of the reciprocals is strictly less than 1.
Original entry on oeis.org
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
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.
-
a[n_] := 1 + Length@ Select[Subsets[Range[2,n], {1, n-1}], Total[1/#] < 1 &]; Array[a, 15] (* Giovanni Resta, Jun 01 2018 *)
Showing 1-2 of 2 results.
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