A307690 Integers with only one prime factor and whose Euler's totient is a perfect biquadrate.

2, 17, 32, 257, 512, 1297, 8192, 65537, 131072, 160001, 331777, 614657, 1336337, 1419857, 2097152, 4477457, 5308417, 8503057, 9834497, 29986577, 33554432, 40960001, 45212177, 59969537, 65610001, 126247697, 193877777, 303595777, 384160001, 406586897, 536870912, 562448657, 655360001

Offset: 1

Author

Bernard Schott, Apr 22 2019

Keywords

• nonn

Comments

An integer q is a term iff q = p^(4*m+1), when p is prime of the form k^4 + 1 and m >= 0, then phi(q) = (k * (k^4+1)^m)^4. The primitive terms of this sequence are the primes of the form p = k^4 + 1, which are exactly in A037896.

Examples

			a(14) = 1419857 = 17^5 and phi(1419857) = 34^4.
		

Crossrefs

Subsequences: A013776 (2^(4*m+1)), A013806 (17^(4*m+1)), A037896 (primes of the form k^4 + 1).

Intersection of A078164 and A246655.

Cf. A054755 (idem with Euler's totient is square).

Programs

Magma

[n:n in [1..10000000]| #PrimeDivisors(n) eq 1 and IsPower(EulerPhi(n),4)]; // Marius A. Burtea, May 09 2019

PARI

isok(n) = isprimepower(n) && ispower(eulerphi(n), 4); \\ Michel Marcus, Apr 23 2019