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

1,2

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

Links

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

Example

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.

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 *)

Prog

(PARI) lista(nn) = {for (n=1, nn, if (!isprime(n) && (eulerphi(n)/n > 2/3), print1(n, ", ")); ); } \\ Michel Marcus, Jul 05 2015
(Magma) [k:k in [1..400]| not IsPrime(k) and EulerPhi(k) gt 2*k/3]; // Marius A. Burtea, Oct 01 2019

Crossrefs

Cf. A166362.

Sequence in context: A334146 A133633 A038509 * A287918 A054550 A107472

Adjacent sequences: A067790 A067791 A067792 * A067794 A067795 A067796

Keyword

nonn

Author

Benoit Cloitre, Feb 07 2002

Extensions

Definition clarified by Michel Marcus, Jul 05 2015

Incorrect Maple program removed by Robert Israel, May 17 2017

Status

approved