A244466 Nonprimes n such that mu(phi(n)) = 1.

1, 9, 14, 18, 22, 46, 94, 118, 166, 214, 334, 358, 422, 454, 526, 662, 694, 718, 766, 926, 934, 958, 961, 1006, 1094, 1126, 1142, 1174, 1382, 1438, 1678, 1718, 1726, 1774, 1822, 1849, 1922, 1934, 1966, 2038, 2246, 2374, 2462, 2566, 2582, 2606, 2614, 2638, 2654, 2734, 2878, 2966, 2974, 3046

Offset

1,2

Comments

Odd terms > 1 are the square of some prime: a(2) = 9 = 3^2, a(23) = 961 = 31^2, a(36) = 1849 = 43^2, ... .

Odd terms > 1 are A078330^2. Even terms are 2*A088179 and 2*A078330^2. - Robert Israel, Aug 01 2014

Links

Michael De Vlieger, Table of n, a(n) for n = 1..11320

Example

9 is not prime, phi(9) = 6 and mu(6) = 1, mu(phi(9)) = 1, so 9 is here.

Maple

filter:= n -> not isprime(n) and numtheory:-mobius(numtheory:-phi(n))=1:
select(filter, [$1..10000]); # Robert Israel, Aug 01 2014

Mathematica

Select[Range[3200],
And[MoebiusMu[EulerPhi[#]] == 1,
   Not[PrimeQ[#]]] &] (* Michael De Vlieger, Aug 06 2014 *)

Prog

(C) a(n) {return mu(phi(n))==1 ? n : ; }
(PARI) for(n=1, 10^4, if(moebius(eulerphi(n))==1, print1(n, ", "))) \\ Derek Orr, Aug 01 2014
(Python)
from sympy import totient, factorint, primefactors, isprime
[n for n in range(1, 10**5) if n == 1 or (not isprime(n) and max(factorint(totient(n)).values()) < 2 and (-1)**len(primefactors(totient(n))) == 1)] # Chai Wah Wu, Aug 06 2014

Crossrefs

Cf. A078330, A088179.

Sequence in context: A305092 A205690 A328246 * A171123 A327896 A302056

Adjacent sequences: A244463 A244464 A244465 * A244467 A244468 A244469

Keyword

nonn,easy

Author

Torlach Rush, Jun 28 2014

Status

approved