cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A212606 Number of distinct sums <= 1 of reciprocals of positive integers <= n.

Original entry on oeis.org

1, 2, 3, 6, 10, 26, 34, 103, 175, 393, 599, 2015, 2551, 8681, 14254, 19620, 34700, 129557, 161272, 595304, 695175, 1094164, 1903859, 7654850, 9413484, 29625309
Offset: 0

Views

Author

Max Alekseyev, May 22 2012

Keywords

Examples

			a(3) = 6 counts numbers { 0, 1/3, 1/2, 2/3, 5/6, 1 }, each of which is can be represented as the sum of reciprocals 1/1, 1/2, and 1/3.

Crossrefs

For distinct sums of distinct reciprocals, see A212607.
Cf. A020473, A092669, A092671, A208480

Extensions

a(24)-a(25) from Dexter Senft, Feb 07 2019

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

Original entry on oeis.org

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

Views

Author

Max Alekseyev, May 23 2012

Keywords

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

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

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

Views

Author

Max Alekseyev, May 23 2012

Keywords

Comments

The number of distinct sums of reciprocals is given by A212606.

Links

Crossrefs

Cf. A212657, A212606, A212607, A020473, A092669, A092671, A208480, A003418.

Extensions

a(24)-a(25) from Alois P. Heinz, Nov 20 2017
a(26)-a(31) from Dexter Senft, Feb 07 2019
Showing 1-3 of 3 results.

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