A107651 Numbers n such that phi(sigma(n)) + phi(phi(n)) = n.

3, 28, 108, 2352, 2544, 7936, 13632, 26736, 209904, 256608, 1394112, 2052864, 2169456, 2490864, 11942400, 18884416, 258072480, 415272960, 2064579840, 3737456640, 3963371520, 4672512000

Offset: 1

Author

Farideh Firoozbakht, May 26 2005

Keywords

• nonn

Comments

If both (3^n-1)/2 and 2*3^n-1 are prime then 48*(2*3^n-1) is in the sequence (the proof is easy). So if n is in the intersection of A028491 and A003307 then 48*(2*3^n-1) is in this sequence. Conjecture: There exist only two such terms, namely 2544 and 209904.

If both (3^n*31-1)/2 and 2*3^n*31-1 are prime then 48*(2*3^n*31-1) is in the sequence (the proof is easy). Conjecture: There exist only three such terms, namely 26736, 2169456, and 26376103844085843261484656.

Examples

			18884416 is in the sequence because phi(sigma(18884416)) + phi(phi(18884416)) = 18884416.
		

Crossrefs

Cf. A003307, A028491, A107652, A107653.

Programs

Mathematica

Do[If[n == EulerPhi[DivisorSigma[1, n]] + EulerPhi[EulerPhi[n]], Print[n] ], {n, 10000000}]

PARI

is(n)=eulerphi(sigma(n))+eulerphi(eulerphi(n))==n \\ Charles R Greathouse IV, Mar 06 2013

Extensions

a(17)-a(22) from Donovan Johnson, Mar 06 2013