A284497 a(n) is the least number such that phi(a(n)) = phi(R(a(n)))/n, where R(n) is the digit reverse of n and phi(n) is the Euler totient function of n.

1, 37, 12, 15, 199, 189, 124, 1004, 18, 168, 126, 12048, 10426, 1358, 11638, 1078, 1011868, 112518, 108018288, 1076768, 1012998

Offset

1,2

Comments

a(22) > 10^9. - Giovanni Resta, Mar 29 2017

Links

Table of n, a(n) for n=1..21.

Formula

Solutions of the equation A000010(n) = A000010(A004086(n))/n.

Example

phi(1) = 1. Its digit reverse is again 1 and phi(1) = 1 = 1 * 1;
phi(37) = 36 and phi(73) = 72 = 2 * 36;
phi(12) = 4 and phi(21) = 12 = 3 * 4;
phi(15) = 8 and phi(51) = 32 = 4 * 8; etc.

Maple

with(numtheory): R:=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 k, n; for k from 1 to q do for n from 1 to q do
if k*phi(n)=phi(R(n)) then print(n); break; fi; od; od; end: P(10^9);

Mathematica

rev[n_] := FromDigits@ Reverse@ IntegerDigits@ n; a[n_] := Block[{k}, For[k = 1, EulerPhi@ rev@ k != n EulerPhi@ k, k++]; k]; Array[a, 18] (* Giovanni Resta, Mar 29 2017 *)

Crossrefs

Cf. A000010, A004086, A284495, A284496, A284498.

Sequence in context: A254324 A356745 A068843 * A033357 A093860 A336480

Adjacent sequences: A284494 A284495 A284496 * A284498 A284499 A284500

Keyword

nonn,more,base

Author

Paolo P. Lava, Mar 28 2017

Extensions

a(19)-a(21) from Giovanni Resta, Mar 29 2017

Status

approved