A083246 - OEIS

%I #9 Nov 16 2017 15:52:23

%S 1,3,8,10,15,18,24,25,30,50,61455

%N Numbers n such that at least one of the following four conditions is satisfied: 1# d(n)=phi(n); 2# d(n)=u(n); 3# phi(n)=u(n), or 4# n=2u(n). Here d(n)=A000005(n) is the number of divisors of n, phi(n)=A000010(n) is Euler's totient and u(n)=A045763(n) is the size of the 'unrelated set'.

%C Is this sequence complete?

%e 1# d(n)=phi(n) holds for {1,3,8,10,18,24,30}, see A020488;

%e 2# d(n)=u(n) holds for {15,25};

%e 3# phi(n)=u(n) holds for {61455};

%e 4# n=2u(n) holds for {30,50}. No more cases below 10^7.

%e {n,d,r,u} values for 11 initial terms are as follows:

%e {1, 1, 1, 0}, {3, 2, 2, 0}, {8, 4, 4, 1}, {10, 4, 4, 3}, {15, 4, 8, 4}, {18, 6, 6, 7}{24, 8, 8, 9}, {25, 3, 20, 3}, {30, 8, 8, 15}, {50, 6, 20, 25}, {61455, 16, 30720, 30720}.

%t Do[r=EulerPhi[n]; d=DivisorSigma[0, n]; u=n-r-d+1; If[Equal[d, r]||Equal[d, u]||Equal[r, u]||Equal[u, n-u], Print[n(*, {d, r, u}*)]], {n, 1, 10000000}]

%o (PARI) is(n)=my(r=eulerphi(n),d=numdiv(n),u=n-r-d+1);d==r||d==u||r==u||2*u==n \\ _Charles R Greathouse IV_, Feb 21 2013

%Y Cf. A000005, A000010, A045763, A073757, A083243, A083244, A083246, A020488.

%K nonn,less

%O 1,2

%A _Labos Elemer_, May 07 2003