A112010 - OEIS

%I #10 Feb 24 2016 20:38:53

%S 24,1064,2592,6520,106434,145166,237165,262535,372780,491520,531765,

%T 546410,566250,636352,12716544,12806910,13666320,15116832,15408692,

%U 17473715,21645616,23473515,23726640,23728264,26722436,26757024,27933192,30537364,30869280,32118177,33452293,34114338,39602752,42262365,44373490

%N Numbers n with even length such that phi(n)=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 n.

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

%t 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}]

%t 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 *)

%Y Cf. A110084, A112009, A112011.

%K base,nonn

%O 1,1

%A _Farideh Firoozbakht_, Aug 26 2005

%E More terms from _Max Alekseyev_, Oct 16 2012