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A307690
Integers with only one prime factor and whose Euler's totient is a perfect biquadrate.
3
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.
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
KEYWORD
nonn
AUTHOR
Bernard Schott, Apr 22 2019
STATUS
approved