A056774 - OEIS

%I #18 Sep 08 2019 10:24:41

%S 6,12,14,18,20,44,62,92,116,164,212,254,332,356,452,524,692,716,764,

%T 932,956,1004,1124,1172,1436,1676,1724,1772,1964,2036,2372,2564,2612,

%U 2636,2732,2876,2972,3044,3236,3644,3812,4052,4076,4124,4196,4412,4892

%N Composite n such that phi(n+2) = phi(n)+2.

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

%C 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.

%H Amiram Eldar, <a href="/A056774/b056774.txt">Table of n, a(n) for n = 1..10000</a>

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

%t Select[Range[5000],CompositeQ[#]&&EulerPhi[#]+2==EulerPhi[#+2]&] (* _Harvey P. Dale_, Jul 10 2017 *)

%o (PARI) isok(n) = !isprime(n) && (eulerphi(n+2) == eulerphi(n)+2); \\ _Michel Marcus_, Aug 30 2019

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

%K nonn

%O 1,1

%A _Labos Elemer_, Aug 17 2000