A247316 Numbers x such that the sum of all their cyclic permutations is equal to that of all cyclic permutations of their Euler totient functions phi(x).

1, 21, 27, 34, 54, 63, 81, 171, 205, 212, 214, 237, 243, 272, 291, 315, 324, 333, 342, 351, 356, 358, 394, 402, 405, 424, 432, 441, 459, 493, 502, 504, 513, 538, 540, 544, 565, 585, 624, 630, 663, 702, 712, 714, 716, 718, 723, 729, 745, 804, 810, 831, 834, 835

Offset

1,2

Comments

The minimum number with all its cyclic permutations belonging to the sequence is 243: 243, 324, 432. But if a "0" is prepended to 54 then it could be considered the minimum one: 054, 405, 540.

Links

Paolo P. Lava, Table of n, a(n) for n = 1..5000

Example

The sum of the cyclic permutations of 171 is 171 + 117 + 711 = 999; phi(171) = 108 and the sum of its cyclic permutations is 108 + 810 + 81 = 999.
The sum of the cyclic permutations of 1863 is 1863 + 3186 + 6318 + 8631 = 19998; phi(1863) = 1188 and the sum of its cyclic permutations is 1188 + 8118 + 8811 + 1881 = 19998.

Maple

with(numtheory):P:=proc(q) local a, b, c, d, k, n;
for n from 1 to q do a:=n; b:=a; c:=ilog10(a);
for k from 1 to c do a:=(a mod 10)*10^c+trunc(a/10); b:=b+a; od;
a:=phi(n); d:=a; c:=ilog10(a);
for k from 1 to c do a:=(a mod 10)*10^c+trunc(a/10); d:=d+a; od;
if d=b then print(n); fi; od; end: P(10^9);

Crossrefs

Cf. A000010, A247315, A247317.

Sequence in context: A103246 A206347 A362008 * A072392 A144415 A098898

Adjacent sequences: A247313 A247314 A247315 * A247317 A247318 A247319

Keyword

nonn,base,easy

Author

Paolo P. Lava, Sep 12 2014

Status

approved