%I #26 Sep 08 2022 08:46:21

%S 2,17,32,257,512,1297,8192,65537,131072,160001,331777,614657,1336337,

%T 1419857,2097152,4477457,5308417,8503057,9834497,29986577,33554432,

%U 40960001,45212177,59969537,65610001,126247697,193877777,303595777,384160001,406586897,536870912,562448657,655360001

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

%C 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.

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

%o (PARI) isok(n) = isprimepower(n) && ispower(eulerphi(n), 4); \\ _Michel Marcus_, Apr 23 2019

%o (Magma) [n:n in [1..10000000]| #PrimeDivisors(n) eq 1 and IsPower(EulerPhi(n),4)]; // _Marius A. Burtea_, May 09 2019

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

%Y Intersection of A078164 and A246655.

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

%K nonn

%O 1,1

%A _Bernard Schott_, Apr 22 2019