A281880 Non-palindromic numbers k such that phi(k) | phi(R(k)), where R(k) is the digits reversal of k.

12, 15, 18, 19, 36, 37, 56, 124, 126, 132, 165, 168, 178, 189, 190, 192, 198, 199, 219, 234, 238, 298, 308, 348, 387, 396, 418, 427, 429, 468, 506, 518, 724, 756, 924, 1004, 1066, 1078, 1089, 1094, 1107, 1143, 1209, 1212, 1314, 1332, 1358, 1364, 1386, 1445, 1452

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..1500

Paolo P. Lava, First 250 terms with the ratio phi(R(k))/phi(k)

Example

a(1) = 12 because phi(21) / phi(12) = 12 / 4 = 3;
a(2) = 15 because phi(51) / phi(15) = 32 / 8 = 4;
a(3) = 18 because phi(81) / phi(18) = 54 / 6 = 9.

Maple

with(numtheory): T:=proc(w) local x, y, z; x:=w; y:=0;
for z from 1 to ilog10(x)+1 do y:=10*y+(x mod 10); x:=trunc(x/10); od; y; end:
P:=proc(q) local n; for n from 1 to q do
if n<>T(n) then if type(phi(T(n))/phi(n), integer) then print(n); fi; fi; od; end: P(10^6);

Mathematica

Select[Range@ 1500, Function[k, And[Reverse@ # != #, Divisible[EulerPhi[FromDigits@ Reverse@ #], EulerPhi@ k]] &@ IntegerDigits@ k]] (* Michael De Vlieger, Feb 04 2017 *)

Crossrefs

Cf. A000010, A004086, A097647, A281879.

Sequence in context: A368995 A188766 A247542 * A153047 A265128 A243021

Adjacent sequences: A281877 A281878 A281879 * A281881 A281882 A281883

Keyword

nonn,easy,base

Author

Paolo P. Lava, Feb 01 2017

Status

approved