A097987 Numbers k such that 4 does not divide phi(k), where phi is Euler's totient function (A000010).

1, 2, 3, 4, 6, 7, 9, 11, 14, 18, 19, 22, 23, 27, 31, 38, 43, 46, 47, 49, 54, 59, 62, 67, 71, 79, 81, 83, 86, 94, 98, 103, 107, 118, 121, 127, 131, 134, 139, 142, 151, 158, 162, 163, 166, 167, 179, 191, 199, 206, 211, 214, 223, 227, 239, 242, 243, 251, 254, 262, 263, 271

Offset

1,2

Comments

The asymptotic density of this sequence is 0 (Dressler, 1975). - Amiram Eldar, Jul 23 2020

Links

Ivan Neretin, Table of n, a(n) for n = 1..10000

Robert E. Dressler, A property of the phi and sigma_j functions, Compositio Mathematica, Vol. 31, No. 2 (1975), pp. 115-118.

Formula

a(n)=1, 2, 4, p^k, 2*p^k, with prime p == 3 (mod 4).

Mathematica

Select[Range@275, ! Divisible[EulerPhi[#], 4] &] (* Ivan Neretin, Aug 24 2016 *)

Prog

(PARI) is(n)=my(o=valuation(n, 2), p); (o<2 && isprimepower(n>>o, &p) && p%4>1) || n<5 \\ Charles R Greathouse IV, Feb 21 2013

Crossrefs

Essentially the same as A066499.

Cf. A000010.

Complement of A172019.

Sequence in context: A015851 A225529 A065156 * A049149 A332555 A304206

Adjacent sequences: A097984 A097985 A097986 * A097988 A097989 A097990

Keyword

nonn

Author

Lekraj Beedassy, Sep 07 2004

Extensions

Corrected and extended by Vladeta Jovovic, Sep 08 2004

Status

approved