A212657 Number of subsets of {1,2,...,n} with the sum of reciprocals <= 1.

1, 2, 3, 5, 8, 14, 26, 46, 83, 151, 276, 503, 921, 1689, 3113, 5730, 10549, 19441, 35868, 66209, 122316, 226157, 418373, 774394, 1434130, 2657246, 4925837, 9135444, 16949660, 31460444, 58415377, 108502932, 201604081, 374708242, 696650259, 1295562800, 2410001851, 4484208954, 8345621293

Offset: 0

Author

Max Alekseyev, May 23 2012

Keywords

• nonn

Comments

The number of distinct sums of reciprocals is given by A212607.

a(n) grows as 2^(b*n) with b=0.911... (Tikhomirov et al. 2017).

Links

• Robert Gerbicz, Table of n, a(n) for n = 0..95
• M. Tikhomirov et al., Sets of unit fractions with sum <=1, MathOverflow, 2017.

Crossrefs

Cf. A212658 (reciprocals can appear multiple times).

Cf. A212606, A212607, A020473, A092669, A092671, A208480.

Programs

PARI

{ A212657(n) = my(L=lcm(vector(n,i,i))); polcoeff( prod(i=1,n, 1+x^(L/i)+O(x^(L+1)) )/(1-x), L); }

Extensions

a(32)-a(35) from Alois P. Heinz, May 23 2012

a(36)-a(95) from Robert Gerbicz, May 23 2012