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 A308219 Number of Egyptian fractions of denominator n which are the sum of 2 unit fractions. 3

%I

%S 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,

%T 18,23,10,29,8,23,18,17,20,34,6,17,20,33,10,34,8,25,28,17,12,41,14,27,

%U 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

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

%C 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).

%H Cyril Banderier, Florian Luca, Francesco Pappalardi, <a href="https://lipn.fr/~cb/Papers/EgyptianFractions.pdf">Numerators of Egyptian fractions</a>, 2019.

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

%e 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.

%Y Cf. A000005, A308220, A308221, A308415.

%K nonn

%O 1,1

%A _Cyril Banderier_, May 15 2019

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Last modified January 21 21:20 EST 2022. Contains 350480 sequences. (Running on oeis4.)