A307854 Numbers k such that phi(r) + phi(s) = k has no solution, where phi is Euler totient function.

1, 15, 27, 35, 39, 51, 63, 69, 75, 77, 87, 91, 95, 99, 115, 119, 123, 125, 135, 143, 147, 153, 155, 159, 171, 175, 183, 187, 189, 195, 203, 207, 215, 219, 231, 235, 237, 243, 245, 247, 249, 255, 259, 267, 275, 279, 285, 287, 291, 299, 303, 305, 309, 315, 319, 323

Offset

1,2

Comments

Problem C1 of Unsolved Problems in Number Theory asks if there are even numbers in this sequence.

References

Richard K. Guy, Unsolved Problems in Number Theory, Springer, 2004, section C1, p. 160.

Links

Table of n, a(n) for n=1..56.

Formula

a(n) = A005277(n-1) + 1 if there are no even numbers in this sequence.

Mathematica

v = Union@ EulerPhi@ Range@ 1680; Complement[Range@ 400, Join[2 v, Plus @@@ Subsets[v, {2}]]] (* Giovanni Resta, Jul 18 2019 *)

Prog

(PARI) is(n)=sum(i=1, n-1, istotient(i)&&istotient(n-i))==0

Crossrefs

Cf. A000010, A002202, A005277, A307853.

Sequence in context: A253056 A091236 A354714 * A053177 A349175 A145195

Adjacent sequences: A307851 A307852 A307853 * A307855 A307856 A307857

Keyword

nonn

Author

Jack Zhang, May 01 2019

Extensions

More terms from Jinyuan Wang, May 03 2019

Status

approved