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

1,1

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).

Links

Table of n, a(n) for n=1..26.

Example

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

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}]

Crossrefs

Cf. A110084, A112009, A112010.

Sequence in context: A309421 A344095 A272690 * A112010 A278650 A046906

Adjacent sequences: A112008 A112009 A112010 * A112012 A112013 A112014

Keyword

base,nonn

Author

Farideh Firoozbakht, Aug 26 2005

Status

approved