

A333838


a(n) is the greatest integer q <= r such that for some r, phi(q) + phi(r) = 2*n.


0



1, 0, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 12, 14, 15, 16, 17, 18, 19, 20, 21, 21, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 34, 38, 39, 40, 41, 42, 43, 43, 45, 46, 47, 48, 49, 50, 51, 52, 53, 53, 55, 56, 57, 58, 59, 60, 60, 61, 62, 64, 65, 66, 64, 68, 68, 70
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OFFSET

1,3


COMMENTS

Paul ErdÅ‘s 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.


REFERENCES

George E. Andrews, Number Theory, Chapter 6, Arithmetic Functions, 61 Combinatorial Study of Phi(n) page 7582, Dover Publishing, NY, 1971.
Daniel Zwillinger, EditorinChief, CRC Standard Mathematical Tables and Formulae, 31st Edition, 2.4.15 Euler Totient pages 128130, Chapman & Hall/CRC, Boca Raton, 2003.


LINKS

Table of n, a(n) for n=1..70.
Eric W. Weisstein's World of Mathematics, Goldbach's Conjecture.
Wikipedia, Goldbach's conjecture
Index entries for sequences related to Goldbach conjecture


MATHEMATICA

mbr = Union@Array[EulerPhi@# &, 500]; a[n_] := Block[{q = n}, While[! MemberQ[mbr, 2 n  EulerPhi@q], q]; q]; Array[a, 70]


CROSSREFS

Cf. A306513, A306513, A333819, A333820.
Sequence in context: A118716 A004177 A004721 * A030544 A141213 A171950
Adjacent sequences: A333835 A333836 A333837 * A333839 A333840 A333841


KEYWORD

nonn


AUTHOR

Robert G. Wilson v, Apr 07 2020


STATUS

approved



