

A067793


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


6



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
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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: A049518 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



