

A212657


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


2



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
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OFFSET

0,2


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.


PROG

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


CROSSREFS

Cf. A212658 (reciprocals can appear multiple times).
Cf. A212606, A212607, A020473, A092669, A092671, A208480.
Sequence in context: A062178 A173282 A178833 * A065955 A196118 A104880
Adjacent sequences: A212654 A212655 A212656 * A212658 A212659 A212660


KEYWORD

nonn,changed


AUTHOR

Max Alekseyev, May 23 2012


EXTENSIONS

a(32)a(35) from Alois P. Heinz, May 23 2012
a(36)a(95) from Robert Gerbicz, May 23 2012


STATUS

approved



