A249396 Composite numbers whose Euler totient divides the sum of the Euler totients of the numbers less than n that are relatively prime to n.

9, 75, 135, 265, 1383, 6585, 17251, 165615, 503111, 856195

Offset: 1

Author

Paolo P. Lava, Oct 27 2014

Keywords

• nonn
• more

Comments

No more terms < 10^6.

Examples

			Numbers coprime to 9 are 1, 2, 4, 5, 7, 8 and phi(9) = 6. Then, phi(1) + phi(2) + phi(4) + phi(5) + phi(7) + phi(8) = 1 + 1 + 2 + 4 + 6 + 4 = 18 and 18/6 = 3.
		

Crossrefs

Cf. A000010, A053570, A249397.

Programs

Maple

with(numtheory): P:=proc(q) local a,k,n; for n from 2 to q do
if not isprime(n) then a:=0;
for k from 1 to n do if gcd(k,n)=1 then a:=a+phi(k); fi; od;
if type(a/phi(n),integer) then print(n); fi; fi; od; end: P(10^9);

PARI

isok(n) = (n!=1) && !isprime(n) && (sum(k=1, n-1, if (gcd(k, n) == 1, eulerphi(k), 0)) % eulerphi(n) == 0); \\ Michel Marcus, Oct 29 2014

Extensions

a(8) from Ray Chandler, Nov 07 2014

a(9)-a(10) from Ray Chandler, Nov 11 2014