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%I #14 Mar 31 2021 12:04:21
%S 12,13,34,48,67,102,123,146,408,449,696,698,942,1002,1030,1234,1367,
%T 4008,5221,6948,10002,10030,10203,10406,12124,12345,12568,40008,40409,
%U 52280,61732,94206,100002,102214,106625,121024,123456,400008,637832,1000002,1000300,1002003
%N Numbers whose palindromization is a perfect power.
%C Palindromization is the function that extends the string representation of a number into a palindrome.
%C Even palindromization is the concatenation of a number and its reversal. Odd palindromization excludes the first digit of the reversal.
%H Michel Marcus, <a href="/A342942/b342942.txt">Table of n, a(n) for n = 1..100</a>
%e 12 is a term because 121 is a square.
%e 13 is a term because 1331 is a cube.
%t Select[Range[10,50000],Or@@(GCD@@Last/@FactorInteger@#>1&/@FromDigits/@(Join[a,Reverse@#]&/@{a=IntegerDigits@#,Most@a}))&] (* _Giorgos Kalogeropoulos_, Mar 30 2021 *)
%o (PARI) rev(x) = strjoin(Vecrev(Str(x)));
%o isok(m) = ispower(eval(Str(m, rev(m)))) || ispower(eval(Str(m, rev(m\10))));
%Y Cf. A075786, A076443, A001597, A002113, A342803.
%K nonn,base
%O 1,1
%A _Michel Marcus_, Mar 30 2021