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

1,1

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.

Links

Table of n, a(n) for n=1..33.

Example

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

Prog

(PARI) isok(n) = isprimepower(n) && ispower(eulerphi(n), 4); \\ Michel Marcus, Apr 23 2019
(Magma) [n:n in [1..10000000]| #PrimeDivisors(n) eq 1 and IsPower(EulerPhi(n), 4)]; // Marius A. Burtea, May 09 2019

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).

Sequence in context: A212742 A178145 A055261 * A100294 A192453 A284779

Adjacent sequences: A307687 A307688 A307689 * A307691 A307692 A307693

Keyword

nonn

Author

Bernard Schott, Apr 22 2019

Status

approved