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.

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

Links

Table of n, a(n) for n=1..35.

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

Cf. A110084, A112009, A112011.

Sequence in context: A344095 A272690 A112011 * A278650 A046906 A130552

Adjacent sequences: A112007 A112008 A112009 * A112011 A112012 A112013

Keyword

base,nonn

Author

Farideh Firoozbakht, Aug 26 2005

Extensions

More terms from Max Alekseyev, Oct 16 2012

Status

approved