A056774 Composite n such that phi(n+2) = phi(n)+2.

6, 12, 14, 18, 20, 44, 62, 92, 116, 164, 212, 254, 332, 356, 452, 524, 692, 716, 764, 932, 956, 1004, 1124, 1172, 1436, 1676, 1724, 1772, 1964, 2036, 2372, 2564, 2612, 2636, 2732, 2876, 2972, 3044, 3236, 3644, 3812, 4052, 4076, 4124, 4196, 4412, 4892

Offset: 1

Author

Labos Elemer, Aug 17 2000

Keywords

• nonn

Comments

Below 100000 no common composite solutions with sigma(n+2)=sigma(n)+2, while prime solutions are common.

phi(x)+2=phi(x+2) is equivalent to cototient(x+2)=cototient(x), so also defines closest numbers with identical value of cototients (A051953), either primes or composites.

Examples

			n=254, phi(254+2) = phi(256) = 128 = phi(254)+2 = 126+2.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000010, A001838, A055458, A015913-A015917, A050507, A054799.

Programs

Mathematica

Select[Range[5000],CompositeQ[#]&&EulerPhi[#]+2==EulerPhi[#+2]&] (* Harvey P. Dale, Jul 10 2017 *)

PARI

isok(n) = !isprime(n) && (eulerphi(n+2) == eulerphi(n)+2); \\ Michel Marcus, Aug 30 2019