A343074 -id:A343074 - cp's OEIS frontend

A342267 Number of partitions of 1/n into n reciprocals of positive integers.

1, 2, 21, 694, 118995, 132891609

Offset: 1

Ilya Gutkovskiy, Mar 07 2021

			a(2) = 2 because we have 1/2 = 1/4 + 1/4 = 1/3 + 1/6.

Cf. A002966, A003167, A004194, A018892, A020327, A020328, A343074, A343214, A369470.

a(6) from Jud McCranie, Sep 02 2021

A369469 a(n) = number of integer solutions to 1 <= x1 < x2 < ... < xn to 1/x1 + ... + 1/xn = (1 - 1/x1) * ... * (1 - 1/xn).

Original entry on oeis.org

1, 1, 1, 24, 293, 9219, 787444

Offset: 1

Max Alekseyev, Jan 23 2024

For any n, A369470(n) >= a(n) >= 1 (see A369607).

Max Muller et al., The diophantine equation \sum_{n=1}^{N} \frac{1}{x_{n}} = \prod_{k=1}^{N} \left(1-\frac{1}{x_{k}} \right), MathOverflow, 2024.

Cf. A006585, A007850, A054377, A085098, A118086, A158649, A164014, A343074, A369470, A369607.

A075461 List of solutions to the Znám problem sorted first by length, then lexicographically.

Original entry on oeis.org

2, 3, 7, 47, 395, 2, 3, 11, 23, 31, 2, 3, 7, 43, 1823, 193667, 2, 3, 7, 47, 403, 19403, 2, 3, 7, 47, 415, 8111, 2, 3, 7, 47, 583, 1223, 2, 3, 7, 55, 179, 24323, 2, 3, 7, 43, 1807, 3263447, 2130014000915, 2, 3, 7, 43, 1807, 3263591, 71480133827, 2, 3, 7, 43

Offset: 1

Eric W. Weisstein, Sep 16 2002

			Starts with A075441(5)=2 5-term solutions 2,3,7,47,395; 2,3,11,23,31, followed by A075441(6)=5 6-term solutions, etc.

Max Alekseyev, Table of n, a(n) for n = 1..934 (flattened list of the n-term solutions for n = 5..8)
J. Janák and L. Skula, On the integers xi for which xi | x1 . . . xi-1 xi . . . xn + 1 holds, Mathematica Slovaca, Vol. 28 (1978), No. 3, 305--310.
J. Sondow and K. MacMillan, Primary pseudoperfect numbers, arithmetic progressions, and the Erdos-Moser equation, Amer. Math. Monthly, 124 (2017) 232-240; arXiv:math/1812.06566 [math.NT], 2018.
Eric Weisstein's World of Mathematics, Znám's Problem
Wikipedia, Znám's problem.

Cf. A006585, A007850, A054377, A075441, A085098, A118086, A158649, A164014, A343074, A369469.

Edited by Max Alekseyev, Jan 25 2024

A343214 Number of compositions (ordered partitions) of 1/n into n reciprocals of positive integers.

Original entry on oeis.org

1, 3, 106, 15259, 13879541, 95073863568

Offset: 1

Ilya Gutkovskiy, Apr 08 2021

			a(2) = 3 because we have 1/2 = 1/4 + 1/4 = 1/3 + 1/6 = 1/6 + 1/3.

Cf. A002967, A048691, A342267, A343074.

a(5)-a(6) from Max Alekseyev, Jan 24 2024

cp's OEIS Frontend

A342267 Number of partitions of 1/n into n reciprocals of positive integers.

Views

Author

Keywords

Examples

Crossrefs

Extensions

A369469 a(n) = number of integer solutions to 1 <= x1 < x2 < ... < xn to 1/x1 + ... + 1/xn = (1 - 1/x1) * ... * (1 - 1/xn).

Views

Author

Keywords

Comments

Links

Crossrefs

A075461 List of solutions to the Znám problem sorted first by length, then lexicographically.

Views

Author

Keywords

Examples

Links

Crossrefs

Extensions

A343214 Number of compositions (ordered partitions) of 1/n into n reciprocals of positive integers.

Views

Author

Keywords

Examples

Crossrefs

Extensions