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

Author

Lekraj Beedassy, Sep 07 2004

Keywords

• nonn

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.

Crossrefs

Essentially the same as A066499.

Cf. A000010.

Complement of A172019.

Programs

Mathematica

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

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

Formula

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

Extensions

Corrected and extended by Vladeta Jovovic, Sep 08 2004