A292283 - OEIS

%I #11 Sep 15 2017 03:37:24

%S 9358,209662,2900878,199550158

%N Numbers n such that f(g(n)) - g(f(n)) = n where f = A001065 and g = A051953.

%C If 2*p is in this sequence for a prime p, then p + 2 is the arithmetic mean of sigma(p + 1) and phi(p + 3). For the first four terms, primes p such that 2*p is in this sequence are 4679, 104831, 1450439, 99775079.

%C a(5) > 3*10^10. - _Giovanni Resta_, Sep 15 2017

%e 9358 is a term because A001065(A051953(9358)) - A051953(A001065(9358)) = 11700 - 2342 = 9358.

%o (PARI) a001065(n) = sigma(n)-n;

%o a051953(n) = n-eulerphi(n);

%o isok(n) = a001065(a051953(n))-a051953(a001065(n))==n;

%Y Cf. A001065, A051953, A291869, A292208.

%K nonn,more

%O 1,1

%A _Altug Alkan_, Sep 13 2017