A083255 Odd composite numbers k such that cototient(k) - phi(k) = k - 2*phi(k) is an odd prime.

165, 195, 5187, 5865, 7395, 10005, 15045, 16215, 21165, 22695, 27285, 37995, 42585, 44115, 50235, 57885, 59415, 60945, 64005, 310845, 346035, 347565, 486795, 635205, 707115, 890445, 979455, 994755, 1049835, 1070535, 1078815, 1083585, 1121745

Offset: 1

Author

Labos Elemer, May 08 2003

Keywords

• nonn

Comments

Quite a number of terms are divisible by 3*5*17 = 255.

Examples

			m = 17425605 = 3*5*23*53*953 is a term since cototient(m) - phi(m) = 9712901 - 8712704 = 197 is an odd prime.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..369 from R. J. Mathar)

Crossrefs

Cf. A000010, A051953, A036798, A067800, A083254.

Programs

Mathematica

Do[s=EulerPhi[n]; c=n-s; If[Greater[c, s]&&PrimeQ[c-s]&&OddQ[c-s]&&!PrimeQ[n], Print[{n, c-s, n/255}]], {n, 1, 10000000}]