A276035 Least k such that n divides phi(k^k) (k > 0).

1, 2, 3, 4, 5, 3, 7, 4, 3, 5, 11, 6, 13, 7, 15, 4, 17, 3, 19, 5, 7, 11, 23, 6, 5, 13, 6, 14, 29, 15, 31, 4, 33, 17, 35, 6, 37, 19, 13, 10, 41, 7, 43, 22, 15, 23, 47, 6, 7, 5, 51, 13, 53, 6, 11, 14, 19, 29, 59, 15, 61, 31, 21, 4, 65, 33, 67, 17, 69, 35

Offset: 1

Author

Altug Alkan, Aug 16 2016

Keywords

• nonn

Comments

The first term that has 3 prime divisors is a(240) = 2*3*5.

Examples

			a(9) = 3 because 9 divides phi(3^3) = 18.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A064447.

Programs

PARI

a(n)=my(k = 1); while(eulerphi(k^k) % n, k++); k;

PARI

a(n)=my(k=1); while(eulerphi(k)*Mod(k,n)^(k-1), k++); k \\ Charles R Greathouse IV, Aug 16 2016

Formula

(log n)/W(log n) < a(n) <= n for n > 1. - Charles R Greathouse IV, Aug 16 2016