A112010 Numbers m with even length such that phi(m)=phi(d_1^d_2*d_3^d_4*...* d_(k-1)^d_k) where d_1 d_2 ... d_k is the decimal expansion of m.

24, 1064, 2592, 6520, 106434, 145166, 237165, 262535, 372780, 491520, 531765, 546410, 566250, 636352, 12716544, 12806910, 13666320, 15116832, 15408692, 17473715, 21645616, 23473515, 23726640, 23728264, 26722436, 26757024, 27933192, 30537364, 30869280, 32118177, 33452293, 34114338, 39602752, 42262365, 44373490

Offset: 1

Author

Farideh Firoozbakht, Aug 26 2005

Keywords

• base
• nonn

Examples

			33452293 is in the sequence because phi(33452293)=phi(3^3*4^5*2^2*9^3).
		

Crossrefs

Cf. A110084, A112009, A112011.

Programs

Mathematica

Do[h = IntegerDigits[n]; k = Length[h]; If[EvenQ[k] && Select[ Range[k/2], h[[2#-1]] == 0 &] == {} && EulerPhi[n]==EulerPhi [Product[h[[2j-1]]^h[[2j]], {j, k/2}]], Print[n]], {n, 31000000}]
epQ[n_]:=Module[{idn=IntegerDigits[n]},EvenQ[Length[idn]]&& FreeQ[ Take[ idn, {1,-1,2}],0] && EulerPhi[n] == EulerPhi[Times@@(#[[1]]^#[[2]]&/@ Partition[ idn,2])]]; Join[Select[Range[10,99],epQ],Select[Range[ 1000,9999], epQ], Select[Range[100000,999999],epQ], Select[Range[ 10000000, 44999999], epQ]] (* Harvey P. Dale, Feb 24 2016 *)

Extensions

More terms from Max Alekseyev, Oct 16 2012