A305678 Solutions x of uphi(x)/x = 2/3, where uphi is the unitary phi function (A047994).

3, 36, 504, 720, 1404, 19656, 28080, 44640, 181440, 195840, 1740960, 7637760, 46085760, 65862720, 105960960, 12884705280, 16729130880, 22826833920, 38463828480, 502503505920, 890246522880, 3377622411509760, 131727274048880640, 55340232208243752960, 2158269056121506365440

Offset: 1

Author

Michel Marcus, Jun 08 2018

Keywords

• nonn

Comments

Apparently, these is a single x, 6, such that uphi(x)/x = 1/3.

Examples

			uphi(3) = 2 so uphi(3)/3 = 2/3;
uphi(36) = 24 so uphi(36)/36 = 2/3.
		

Links

• Tomohiro Yamada, An analog of perfect numbers involving the unitary totient function, arXiv:1806.00647 [math.NT], 2018.

Crossrefs

Cf. A047994 (uphi), A030163 (uphi(x)/x = 1/2).

Programs

PARI

solve_uphi(2, 3, 10^40) \\ see A030163