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

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

1,1

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).

Links

Table of n, a(n) for n=1..100.

Cyril Banderier, Florian Luca, Francesco Pappalardi, Numerators of Egyptian fractions, 2019.

Formula

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

Example

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.

Crossrefs

Cf. A000005, A308220, A308221, A308415.

Sequence in context: A249910 A025511 A224367 * A288758 A210936 A140203

Adjacent sequences: A308216 A308217 A308218 * A308220 A308221 A308222

Keyword

nonn

Author

Cyril Banderier, May 15 2019

Status

approved