A069043 -id:A069043 - cp's OEIS frontend

A038509 Composite numbers congruent to +-1 mod 6.

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, 385

Offset: 1

Jeff Burch

Or, composite numbers with smallest prime factor >= 5.
Or, nonprime numbers n such that binomial(n+3, 3) mod n == 1. - Hieronymus Fischer, Sep 30 2007
Note that the primes > 3 are congruent to +-1 mod 6.
This sequence differs from A067793 (composite n such that phi(n) > 2n/3) starting at 385. Numbers in this sequence but not in A067793 are 385, 455, 595, 665, 805, 1015, 1085, 1925, 2275, 2695, etc. See A069043. - R. J. Mathar, Jun 08 2008 and Zak Seidov, Nov 02 2011
Intersection of A002808 and A007310. - Reinhard Zumkeller, Jun 30 2012
The product (24/25) * (36/35) * (48/49) * (54/55) * (66/65) * (78/77) * (84/85) * (90/91) * ... * ((6*k)/a(n)) * ... = Pi^2/(6*sqrt(3)), where 6*k is the nearest number to a(n), with k in A067611 but not in A002822. (See A258414.) - Dimitris Valianatos, Mar 27 2017

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A171993 (nonprimes of the form 3*k+-1).
Cf. A000040, A133620-A133625, A133630, A133634-A133636.
Cf. A133873, A133883, A133880, A133890, A133900, A133910.
Cf. A069043, A067793 (composite n such that phi(n) > 2n/3).

a038509 n = a038509_list !! (n-1)
a038509_list = [x | x <- a002808_list, gcd x 6 == 1]
-- Reinhard Zumkeller, Aug 05 2014, Jun 30 2012

A038509 := proc(n)
    option remember;
    if n = 1 then
        25;
    else
        for a from procname(n-1)+1 do
            if not isprime(a) and modp(a,6) in {1,5} then
                return a;
            end if;
        end do:
    end if;
end proc:
seq(A038509(n),n=1..30) ; # R. J. Mathar, Feb 28 2020

Select[Range[1000], FactorInteger[#][[1,1]] >= 5 && ! PrimeQ[#] &] (* Robert G. Wilson v, Dec 19 2009 *)
With[{nn=400},Select[Rest[Complement[Range[nn],Prime[Range[ PrimePi[ nn]]]]], MemberQ[ {1,5},Mod[#,6]]&]] (* Harvey P. Dale, Feb 21 2013 *)
Select[Range[400],CompositeQ[#]&&MemberQ[{1,5},Mod[#,6]]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, May 13 2019 *)

is(n)=gcd(n,6)==1 && !isprime(n) && n>7 \\ Charles R Greathouse IV, Nov 20 2012

a(n) ~ 3n. - Charles R Greathouse IV, Nov 20 2012

More terms from Robert G. Wilson v, Dec 19 2009

Entry revised by N. J. A. Sloane, Dec 31 2011, at the suggestion of Gary Detlefs

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

Original entry on oeis.org

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

Benoit Cloitre, Feb 07 2002

nonn

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

			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.

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

Cf. A166362.

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

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

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

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

Definition clarified by Michel Marcus, Jul 05 2015

Incorrect Maple program removed by Robert Israel, May 17 2017

cp's OEIS Frontend

A038509 Composite numbers congruent to +-1 mod 6.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Haskell

Maple

Mathematica

PARI

Formula

Extensions