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.

A308219 Number of Egyptian fractions of denominator n which are the sum of 2 unit fractions.

Original entry on oeis.org

2, 4, 5, 7, 6, 10, 6, 11, 10, 12, 8, 17, 6, 13, 14, 16, 8, 20, 8, 21, 17, 14, 10, 27, 12, 15, 18, 23, 10, 29, 8, 23, 18, 17, 20, 34, 6, 17, 20, 33, 10, 34, 8, 25, 28, 17, 12, 41, 14, 27, 20, 27, 10, 35, 24, 36, 21, 18, 14, 51, 6, 18, 33, 32, 22, 36, 8, 30, 25, 39, 14, 54, 6, 17, 33, 30, 25, 39, 12, 49, 28, 18, 14, 60, 22, 19, 25, 39, 14, 58, 20, 29, 21, 21, 24, 59, 8, 32, 36, 48
Offset: 1

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Author

Cyril Banderier, May 15 2019

Keywords

Comments

a(n) is the number of fractions of denominator n which are the sum of two unit fractions: m/n = 1/r + 1/s (m and n not necessarily coprime).

Examples

			a(2)=4, as there are 4 fractions with denominator 4 which are the sums of 2 unit fractions: 1/2 = 1/4 + 1/4, 2/2 = 1/2 + 1/2, 3/2 = 1/1 + 1/2, 4/2 = 1/1 + 1/1.

Links

Crossrefs

Cf. A000005, A308220, A308221, A308415.

Formula

For p prime, a(p) = 2 + tau(p+1) with tau = A000005.

A308220 Number of irreducible Egyptian fractions of denominator n which are the sum of 2 unit fractions.

Original entry on oeis.org

2, 2, 3, 3, 4, 3, 4, 4, 5, 4, 6, 4, 4, 5, 5, 5, 6, 5, 6, 6, 8, 4, 8, 6, 6, 7, 8, 7, 8, 6, 6, 7, 7, 7, 10, 7, 4, 7, 11, 8, 8, 7, 6, 8, 9, 5, 10, 9, 8, 9, 9, 9, 8, 7, 12, 9, 10, 6, 12, 9, 4, 8, 11, 9, 12, 9, 6, 10, 12, 8, 12, 10, 4, 9, 13, 10, 13, 7, 10, 11, 10, 6, 12, 12, 10, 9, 12, 10, 12, 10, 10, 9, 10, 7, 12, 11, 6, 11, 13, 12
Offset: 1

Views

Author

Cyril Banderier, May 15 2019

Keywords

Examples

			There are a(2)=2 irreducible fractions with denominator n=2 which are sums of 2 unit fractions: 1/2 = 1/4 + 1/4 and 3/2 = 1/1 + 1/2.

Links

Crossrefs

Cf. A308219, A308221, A308415.

Formula

For p prime, a(p) = number_of_divisors(p+1).

A308415 Number of irreducible Egyptian fractions of denominator n which are the sum of 3 unit fractions.

Original entry on oeis.org

3, 3, 5, 5, 8, 5, 10, 8, 11, 8, 13, 8, 15, 10, 13, 12, 18, 11, 19, 14, 19, 13, 22, 14, 22, 15, 22, 18, 24, 13, 25, 20, 23, 18, 28, 18, 25, 20, 28, 22, 28, 19, 29, 24, 29, 20, 33, 24, 35, 23, 32, 27, 33, 22, 42, 28, 35, 24, 38, 24, 30, 26, 38, 31
Offset: 1

Views

Author

Cyril Banderier, May 25 2019

Keywords

Examples

			There are a(2)=3 irreducible fractions with denominator n=2 which are the sums of 3 unit fractions: 1/2 = 1/8 + 1/8 + 1/4 and 3/2 = 1/2 + 1/2 + 1/2, and 5/2 = 1/1 + 1/1 + 1/2.

Links

Crossrefs

Cf. A308219, A308220, A308221.
Showing 1-3 of 3 results.

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