A112011 Numbers n with even length such that phi(n)=phi(d_1^d_2)*phi(d_3^d_4) *...*phi(d_(k-1)^d_k) where d_1 d_2 ... d_k is the decimal expansion of n.

24, 1064, 2592, 6520, 9234, 145166, 245344, 296480, 372780, 491520, 531765, 546410, 566250, 664062, 12806910, 12826710, 14466530, 15408692, 15621268, 17473715, 19946352, 22297520, 23256720, 30537364, 30869280, 32118177

Offset: 1

Author

Farideh Firoozbakht, Aug 26 2005

Keywords

• base
• nonn

Comments

For the third term we have the relation 2592=2^5*9^2. So phi(2592)=phi(2^5*9^2)=phi(2^5)*phi(9^2).

Examples

			39602752 is in the sequence because phi(39602752)=
phi(3^9)*phi(6^0)*phi(2^7)*phi(5^2).
		

Crossrefs

Cf. A110084, A112009, A112010.

Programs

Mathematica

Do[h = IntegerDigits[n]; k = Length[h]; If[EvenQ[k] && Select[ Range[k/2], h[[2#-1]] == 0 &] == {} && EulerPhi[n]== Product[EulerPhi[h[[2j-1]]^h[[2j]]], {j, k/2}], Print[n]], {n, 35000000}]