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Numbers k for which A053669(6*k) [the smallest prime not dividing 6k] is of the form 6m-1.
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%I #12 Dec 04 2022 08:33:11

%S 1,2,3,4,6,7,8,9,11,12,13,14,16,17,18,19,21,22,23,24,26,27,28,29,31,

%T 32,33,34,35,36,37,38,39,41,42,43,44,46,47,48,49,51,52,53,54,56,57,58,

%U 59,61,62,63,64,66,67,68,69,70,71,72,73,74,76,77,78,79,81,82,83,84,86,87,88,89,91,92,93,94

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

%C The asymptotic density of this sequence is 6 * Sum_{p prime, p == 5 (mod 6)} ((p-1)/(Product_{q prime, q <= p} q)) = 0.8261626908... . - _Amiram Eldar_, Dec 04 2022

%F {k | A053669(6*k) == 5 (mod 6)}.

%e 35 is present as 6*35 = 210 = 2*3*5*7, and the first nondividing prime is 11, which is of the form 6m+5. This is the first multiple of 5 in this sequence.

%e 385 is not present as 6*385 = 2310 = 2*3*5*7*11, and the first nondividing prime is 13, which is of the form 6m+1, not of 6m+5.

%t f[n_] := Module[{p = 2}, While[Divisible[n, p], p = NextPrime[p]]; p]; Select[Range[100], Mod[f[6*#], 6] == 5 &] (* _Amiram Eldar_, Dec 04 2022 *)

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

%Y Cf. A053669, A358847 (characteristic function), A358848 (complement).

%K nonn

%O 1,2

%A _Antti Karttunen_, Dec 03 2022