OFFSET
1,1
COMMENTS
Paul Erdős and Leo Moser conjectured that, for any even numbers 2*n, there exist integers q and r such that phi(q) + phi(r) = 2*n. Therefore, they conjecture a(n) > 0 for all ns.
REFERENCES
George E. Andrews, Number Theory, Chapter 6, Arithmetic Functions, 6-1 Combinatorial Study of Phi(n) page 75-82, Dover Publishing, NY, 1971.
Daniel Zwillinger, Editor-in-Chief, CRC Standard Mathematical Tables and Formulae, 31st Edition, 2.4.15 Euler Totient pages 128-130, Chapman & Hall/CRC, Boca Raton, 2003.
LINKS
Eric W. Weisstein's World of Mathematics, Goldbach's Conjecture.
Wikipedia, Goldbach's conjecture
EXAMPLE
a(2) = 6 because for the pairs {q, r} the following pairs when phi(q) + phi(r) = 4; {3,3}, {3,4}, {3,6}, {4,4}, {4,6}, {6,6}.
MATHEMATICA
f[n_] := Block[{c = 0, q = 1}, While[q < 12n, epq = EulerPhi[q]; r = 12n + 25; While[r >= q, If[ epq + EulerPhi[r] == 2 n, c++; AppendTo[lst, {q, r}]]; r--]; q++]; c]; Array[f, 60]
CROSSREFS
KEYWORD
nonn
AUTHOR
Robert G. Wilson v, Apr 06 2020
STATUS
approved