A328276 The number of solutions to phi(x) = rad(x)^n, where phi is the Euler totient function (A000010) and rad is the squarefree kernel function (A007947).

3, 6, 16, 85, 969

Offset: 1

Author

Amiram Eldar, Oct 10 2019

Keywords

• nonn
• more

Comments

The author informs me that because there of an error in one of the references, a(4) is > 85. - N. J. A. Sloane, Nov 23 2019

Examples

			a(1) = 3 since there are only 3 solutions to phi(x) = rad(x): x = 1, 4, and 18.
a(2) = 6 since there are only 6 solutions to phi(x) = rad(x)^2: x = 1, 8, 108, 250, 6174, and 41154 (the terms of A211413).
		

Links

• Jean-Marie De Konick and Stefan Gubo, When the totient is the product of the squared prime divisors: problem 10966, American Mathematical Monthly, Vol. 111, No. 6 (2004), p. 536.
• Jean-Marie De Koninck, Florian Luca and A. Sankaranarayanan, Positive integers whose Euler function is a power of their kernel function, Rocky Mountain Journal of Mathematics, Vol. 36, No. 1 (2006), pp. 81-96, alternative link.

Crossrefs

Cf. A000010, A007947, A105261, A211413, A328274, A328275.