VOOZH about

URL: https://oeis.org/A308219

⇱ A308219 - OEIS

login
A308219
Number of Egyptian fractions of denominator n which are the sum of 2 unit fractions.
3
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
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
KEYWORD
nonn
AUTHOR
Cyril Banderier, May 15 2019
STATUS
approved