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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified November 26 17:52 EST 2021. Contains 349343 sequences. (Running on oeis4.)