A067793 Nonprimes n such that phi(n) > 2n/3.

1, 25, 35, 49, 55, 65, 77, 85, 91, 95, 115, 119, 121, 125, 133, 143, 145, 155, 161, 169, 175, 185, 187, 203, 205, 209, 215, 217, 221, 235, 245, 247, 253, 259, 265, 275, 287, 289, 295, 299, 301, 305, 319, 323, 325, 329, 335, 341, 343, 355, 361, 365, 371, 377, 391, 395, 403, 407, 413, 415, 425, 427

Offset: 1

Author

Benoit Cloitre, Feb 07 2002

Keywords

• nonn

Comments

Differs from A038509 in the first entry and in addition as documented in A069043. - R. J. Mathar, Sep 30 2008

It appears that a(n) lists the composite values of n which satisfy the condition sum(k^2,k=1..n) mod n = A000330(n) mod n = A215573(n) = 0. - Gary Detlefs, Nov 16 2011

Conjecture: Odd composite n such that (n^2 + 8) mod 3 = 0. (All primes > 3 meet this criterion). - Gary Detlefs, May 03 2012

Both conjectures are wrong. The first counterexample is 385. - Robert Israel, May 17 2017

The semiprime numbers p * q, p, q > 3, are terms. - Marius A. Burtea, Oct 01 2019

Examples

			10 is not in the list because phi(10) = 4 < 2*10/3. 25 is in the list because phi(25) = 20 > 2*25/3.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A166362.

Programs

Magma

[k:k in [1..400]| not IsPrime(k) and EulerPhi(k) gt 2*k/3]; // Marius A. Burtea, Oct 01 2019

Maple

select(n -> not isprime(n) and numtheory:-phi(n) > 2*n/3, [$1..1000]); # Robert Israel, May 17 2017

Mathematica

Select[Range[1000], ! PrimeQ[#] && EulerPhi[#] > 2 #/3 &] (* T. D. Noe, Nov 02 2011 *)

PARI

lista(nn) = {for (n=1, nn, if (!isprime(n) && (eulerphi(n)/n > 2/3), print1(n, ", ")););} \\ Michel Marcus, Jul 05 2015

Extensions

Definition clarified by Michel Marcus, Jul 05 2015

Incorrect Maple program removed by Robert Israel, May 17 2017