A078596 Numbers m such that there is at least one pair (x,y) 1 <= x <= y <= m such that 1/x + 1/y + 1/m = 1/phi(m).

6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 84, 90, 96, 108, 120, 126, 132, 144, 150, 162, 168, 180, 192, 198, 210, 216, 234, 240, 252, 264, 270, 276, 288, 294, 300, 306, 324, 330, 336, 360, 378, 384, 396, 420, 432, 450, 462, 468, 480, 486, 504, 528, 540, 546

Offset

1,1

Comments

It seems that necessarily a(n) == 0 (mod 6).

This is not true. The terms that are not divisible by 6 are 3850, 7700, 13300, 14210, 15400, ... . - Amiram Eldar, Jun 24 2022

Links

Amiram Eldar, Table of n, a(n) for n = 1..500

Example

From Amiram Eldar, Jun 24 2022: (Start)
m = 6 is a term since for x = y = 6 we have 1/x + 1/y + 1/m = 1/6 + 1/6 + 1/6 = 1/2 = 1/phi(6).
m = 3850 is a term since for x = 3300 and y = 3696 we have 1/x + 1/y + 1/m = 1/3300 + 1/3696 + 1/3850 = 1/1200 = 1/phi(3850). (End)

Mathematica

q[m_] := Module[{s = 1/EulerPhi[m] - 1/m, k}, AnyTrue[Range[m], 1/# < s && IntegerQ[k = 1/(s - 1/#)] && 0 < k <= m &]]; Select[Range[600], q] (* Amiram Eldar, Jun 24 2022 *)

Crossrefs

Cf. A000010.

Sequence in context: A175130 A008458 A008588 * A187389 A085129 A236240

Adjacent sequences: A078593 A078594 A078595 * A078597 A078598 A078599

Keyword

nonn

Author

Benoit Cloitre, Dec 08 2002

Extensions

3 missing terms inserted and more terms added by Amiram Eldar, Jun 24 2022

Status

approved