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A112010
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.
3
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
1,1
EXAMPLE
33452293 is in the sequence because phi(33452293)=phi(3^3*4^5*2^2*9^3).
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 *)
CROSSREFS
KEYWORD
base,nonn
AUTHOR
Farideh Firoozbakht, Aug 26 2005
EXTENSIONS
More terms from Max Alekseyev, Oct 16 2012
STATUS
approved