A247317 Numbers x such that the sum of all their cyclic permutations is equal to that of all cyclic permutations of sigma(x) and all cyclic permutations of Euler totient function phi(x).

1, 2907, 3339, 3726, 4293, 4371, 4614, 5049, 5319, 5607, 5751, 6291, 17901, 18009, 18441, 19413, 20349, 20655, 20943, 21219, 21267, 21573, 21627, 22137, 22191, 23355, 24831, 25647, 25731, 26019, 26145, 26163, 27405, 27537, 28035, 28215, 28227, 28305, 29601, 30429

Offset: 1

Author

Paolo P. Lava, Sep 12 2014

Keywords

• nonn
• base
• easy

Comments

Intersection of A247315 and A247316.

All numbers appear to be multiples of 3.

Big steps between a(135) and a(136), a(1387) and a(1388),...

Examples

			The sum of the cyclic permutations of 4371 is 4371 + 1437 + 7143 + 3714 = 16667; sigma(4371) = 6144 and the sum of its cyclic permutations is 6144 + 4614 + 4461 + 1446 = 16667; phi(4371) = 2760 and the sum of its cyclic permutations is2760+276+6027+7602 = 16667.
The sum of the cyclic permutations of 24831 is 24831 + 12483 + 31248 + 83124 + 48312 = 199998; sigma(24831) = 37440 and the sum of its cyclic permutations is 37440 + 3744 + 40374 + 44037 + 74403 = 199998; phi(24831) = 15840 and the sum of its cyclic permutations is 15840 + 1584 + 40158 + 84015 + 58401 = 199998.
		

Links

• Paolo P. Lava, Table of n, a(n) for n = 1..1500
• Paolo P. Lava, Plot of the first 1500 terms of the sequence

Crossrefs

A000010, A000203, A247315, A247316.

Programs

Maple

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