login
A067793
Nonprimes n such that phi(n) > 2n/3.
5
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
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
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