A083246 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'.

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

Offset

1,2

Comments

Is this sequence complete?

Links

Table of n, a(n) for n=1..11.

Example

1# d(n)=phi(n) holds for {1,3,8,10,18,24,30}, see A020488;
2# d(n)=u(n) holds for {15,25};
3# phi(n)=u(n) holds for {61455};
4# n=2u(n) holds for {30,50}. No more cases below 10^7.
{n,d,r,u} values for 11 initial terms are as follows:
{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}.

Mathematica

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}]

Prog

(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

Crossrefs

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

Sequence in context: A184870 A073547 A047356 * A023492 A022801 A128699

Adjacent sequences: A083243 A083244 A083245 * A083247 A083248 A083249

Keyword

nonn,less

Author

Labos Elemer, May 07 2003

Status

approved