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

1,1

Comments

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

Links

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

Example

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

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}]

Crossrefs

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

Sequence in context: A261758 A252725 A168355 * A259283 A319502 A270175

Adjacent sequences: A083252 A083253 A083254 * A083256 A083257 A083258

Keyword

nonn

Author

Labos Elemer, May 08 2003

Status

approved