A211134 -id:A211134 - cp's OEIS frontend

A201643 John Leech's example of a set of eleven distinct odd numbers the sum of whose reciprocals is 1.

3, 5, 7, 9, 15, 21, 27, 35, 63, 105, 135

Offset: 1

N. J. A. Sloane, Dec 03 2011

There are smaller sets - see for example A201644.

One of 17 possible sets of eleven numbers of the form 3^alpha 5^beta 7^gamma whose sum of reciprocals is 1. The 17 solutions are given in A211118 - A211134. - N. J. A. Sloane, Apr 02 2012

R. K. Guy, Unsolved Problems in Number Theory (UPINT), Section D11.

Burshtein, Nechemia. On distinct unit fractions whose sum equals 1. Discrete Math. 5 (1973), 201--206. MR0314738 (47 #3290)
Burshtein, Nechemia. All the solutions of the equation Sum_{i=1..11} 1/x_i = 1 in distinct integers of the form x_i = 3^alpha 5^beta 7^gamma. Discrete Math. 308 (2008), no. 18, 4286--4292. MR2427761 (2009e:11061)
The Prime Puzzles and Problems Connection, Problem 35.
Index entries for sequences related to Egyptian fractions

Cf. A201643, A201644, A201646, A201647, A201648, A201649.

A211118 One of 17 possible sets of eleven numbers of the form 3^alpha 5^beta 7^gamma whose sum of reciprocals is 1.

Original entry on oeis.org

3, 5, 7, 9, 15, 21, 25, 27, 75, 125, 23625

Offset: 1

N. J. A. Sloane, Apr 02 2012

Nechemia Burshtein, All the solutions of the equation Sum_{i=1..11} 1/x_i = 1 in distinct integers of the form x_i = 3^alpha 5^beta 7^gamma, Disc. Math. (2008) Vol. 308, No. 18, 4286-4292. MR2427761 (2009e:11061)

The 17 solutions are given in A201643, A211118-A211132, A211134.

Cf. A201644, A201646, A201647, A201648, A201649.

A211132 One of 17 possible sets of eleven numbers of the form 3^alpha 5^beta 7^gamma whose sum of reciprocals is 1.

Original entry on oeis.org

3, 5, 7, 9, 15, 21, 27, 35, 45, 135, 315

Offset: 1

N. J. A. Sloane, Apr 02 2012

Nechemia Burshtein, All the solutions of the equation Sum_{i=1..11} 1/x_i = 1 in distinct integers of the form x_i = 3^alpha 5^beta 7^gamma, Disc. Math. (2008) Vol. 308, No. 18, 4286-4292. MR2427761 (2009e:11061)

The 17 solutions are given in A201643, A211118-A211132, A211134.

Cf. A201644, A201646, A201647, A201648, A201649.

A211135 One of 15 possible sets of eleven odd numbers, not all of the form 3^alpha 5^beta 7^gamma, whose sum of reciprocals is 1.

Original entry on oeis.org

3, 5, 7, 9, 15, 11, 33, 35, 45, 55, 77, 105

Offset: 1

N. J. A. Sloane, Apr 02 2012

Nechemia Burshtein, All the solutions of the equation Sum_{i=1..11} 1/x_i = 1 in distinct integers of the form x_i = 3^alpha 5^beta 7^gamma, Disc. Math. (2008) Vol. 308, No. 18, 4286-4292. MR2427761 (2009e:11061)

Five of the 15 solutions are shown in A211135-A211139. Cf. A211118-A211134, A201643, A201644, A201646, A201647, A201648, A201649.

A211139 One of 15 possible sets of eleven odd numbers, not all of the form 3^alpha 5^beta 7^gamma, whose sum of reciprocals is 1.

Original entry on oeis.org

3, 5, 7, 9, 13, 19, 21, 35, 315, 325, 1425

Offset: 1

N. J. A. Sloane, Apr 02 2012

Nechemia Burshtein, All the solutions of the equation Sum_{i=1..11} 1/x_i = 1 in distinct integers of the form x_i = 3^alpha 5^beta 7^gamma, Disc. Math. (2008) Vol. 308, No. 18, 4286-4292. MR2427761 (2009e:11061)

Five of the 15 solutions are shown in A211135-A211139. Cf. A211118-A211134, A201643, A201644, A201646, A201647, A201648, A201649.

A211119 One of 17 possible sets of eleven numbers of the form 3^alpha 5^beta 7^gamma whose sum of reciprocals is 1.

Original entry on oeis.org

3, 5, 7, 9, 15, 21, 25, 35, 63, 75, 1575

Offset: 1

N. J. A. Sloane, Apr 02 2012

Nechemia Burshtein, All the solutions of the equation Sum_{i=1..11} 1/x_i = 1 in distinct integers of the form x_i = 3^alpha 5^beta 7^gamma, Disc. Math. (2008) Vol. 308, No. 18, 4286-4292. MR2427761 (2009e:11061)

The 17 solutions are given in A201643, A211118-A211132, A211134.

Cf. A201644, A201646, A201647, A201648, A201649.

A211120 One of 17 possible sets of eleven numbers of the form 3^alpha 5^beta 7^gamma whose sum of reciprocals is 1.

Original entry on oeis.org

3, 5, 7, 9, 15, 21, 25, 35, 45, 175, 525

Offset: 1

N. J. A. Sloane, Apr 02 2012

Nechemia Burshtein, All the solutions of the equation Sum_{i=1..11} 1/x_i = 1 in distinct integers of the form x_i = 3^alpha 5^beta 7^gamma, Disc. Math. (2008) Vol. 308, No. 18, 4286-4292. MR2427761 (2009e:11061)

The 17 solutions are given in A201643, A211118-A211132, A211134.

Cf. A201644, A201646, A201647, A201648, A201649.

A211121 One of 17 possible sets of eleven numbers of the form 3^alpha 5^beta 7^gamma whose sum of reciprocals is 1.

Original entry on oeis.org

3, 5, 7, 9, 15, 21, 25, 27, 75, 135, 1575

Offset: 1

N. J. A. Sloane, Apr 02 2012

Nechemia Burshtein, All the solutions of the equation Sum_{i=1..11} 1/x_i = 1 in distinct integers of the form x_i = 3^alpha 5^beta 7^gamma, Disc. Math. (2008) Vol. 308, No. 18, 4286-4292. MR2427761 (2009e:11061)

The 17 solutions are given in A201643, A211118-A211132, A211134.

Cf. A201644, A201646, A201647, A201648, A201649.

A211122 One of 17 possible sets of eleven numbers of the form 3^alpha 5^beta 7^gamma whose sum of reciprocals is 1.

Original entry on oeis.org

3, 5, 7, 9, 15, 21, 25, 35, 45, 225, 315

Offset: 1

N. J. A. Sloane, Apr 02 2012

Nechemia Burshtein, All the solutions of the equation Sum_{i=1..11} 1/x_i = 1 in distinct integers of the form x_i = 3^alpha 5^beta 7^gamma, Disc. Math. (2008) Vol. 308, No. 18, 4286-4292. MR2427761 (2009e:11061)

The 17 solutions are given in A201643, A211118-A211132, A211134.

Cf. A201644, A201646, A201647, A201648, A201649.

A211123 One of 17 possible sets of eleven numbers of the form 3^alpha 5^beta 7^gamma whose sum of reciprocals is 1.

Original entry on oeis.org

3, 5, 7, 9, 15, 21, 25, 35, 63, 105, 225

Offset: 1

N. J. A. Sloane, Apr 02 2012

Nechemia Burshtein, All the solutions of the equation Sum_{i=1..11} 1/x_i = 1 in distinct integers of the form x_i = 3^alpha 5^beta 7^gamma, Disc. Math. (2008) Vol. 308, No. 18, 4286-4292. MR2427761 (2009e:11061)

The 17 solutions are given in A201643, A211118-A211132, A211134.

Cf. A201644, A201646, A201647, A201648, A201649.

cp's OEIS Frontend

A201643 John Leech's example of a set of eleven distinct odd numbers the sum of whose reciprocals is 1.

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A211118 One of 17 possible sets of eleven numbers of the form 3^alpha 5^beta 7^gamma whose sum of reciprocals is 1.

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A211132 One of 17 possible sets of eleven numbers of the form 3^alpha 5^beta 7^gamma whose sum of reciprocals is 1.

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A211135 One of 15 possible sets of eleven odd numbers, not all of the form 3^alpha 5^beta 7^gamma, whose sum of reciprocals is 1.

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A211139 One of 15 possible sets of eleven odd numbers, not all of the form 3^alpha 5^beta 7^gamma, whose sum of reciprocals is 1.

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A211119 One of 17 possible sets of eleven numbers of the form 3^alpha 5^beta 7^gamma whose sum of reciprocals is 1.

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A211120 One of 17 possible sets of eleven numbers of the form 3^alpha 5^beta 7^gamma whose sum of reciprocals is 1.

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Author

Keywords

Links

Crossrefs

A211121 One of 17 possible sets of eleven numbers of the form 3^alpha 5^beta 7^gamma whose sum of reciprocals is 1.

Views

Author

Keywords

Links

Crossrefs

A211122 One of 17 possible sets of eleven numbers of the form 3^alpha 5^beta 7^gamma whose sum of reciprocals is 1.

Views

Author

Keywords

Links

Crossrefs

A211123 One of 17 possible sets of eleven numbers of the form 3^alpha 5^beta 7^gamma whose sum of reciprocals is 1.

Views

Author

Keywords

Links

Crossrefs