A358848 - OEIS

%I #12 Dec 04 2022 08:33:07

%S 5,10,15,20,25,30,40,45,50,55,60,65,75,80,85,90,95,100,110,115,120,

%T 125,130,135,145,150,155,160,165,170,180,185,190,195,200,205,215,220,

%U 225,230,235,240,250,255,260,265,270,275,285,290,295,300,305,310,320,325,330,335,340,345,355,360,365,370,375,380,385

%N Numbers k for which A053669(6*k) [the smallest prime not dividing 6k] is of the form 6m+1.

%C Contains only multiples of 5. Differs from A067761 by including for example 385 = 5*7*11, which is not present in A067761.

%C The asymptotic density of this sequence is 6 * Sum_{p prime, p == 1 (mod 6)} ((p-1)/(Product_{q prime, q <= p} q)) = 0.1738373091... . - _Amiram Eldar_, Dec 04 2022

%F {k | A053669(6*k) == 1 (mod 6)}.

%e 35 is not present as 6*35 = 210 = 2*3*5*7, and the first nondividing prime is 11, which is of the form 6m+5, not of 6m+1.

%e 385 is present as 6*385 = 2310 = 2*3*5*7*11, and the first nondividing prime is 13, which is of the form 6m+1.

%t f[n_] := Module[{p = 2}, While[Divisible[n, p], p = NextPrime[p]]; p]; Select[Range[400], Mod[f[6*#], 6] == 1 &] (* _Amiram Eldar_, Dec 04 2022 *)

%o (PARI) isA358848(n) = !A358847(n);

%Y Positions of 0's in A358847. Complement is A358849. Subsequence of A008587.

%Y Not the same as A067761.

%Y Cf. A053669.

%K nonn

%O 1,1

%A _Antti Karttunen_, Dec 03 2022