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