A353530 - OEIS

%I #12 Jul 25 2022 15:52:25

%S 6,12,18,24,36,42,48,54,66,72,78,84,96,102,108,114,126,132,138,144,

%T 156,162,168,174,186,192,198,204,216,222,228,234,246,252,258,264,276,

%U 282,288,294,306,312,318,324,336,342,348,354,366,372,378,384,396,402,408,414,426,432,438,444,456,462,468,474,486,492

%N Numbers k such that the smallest prime that does not divide them is of the form 4m+1.

%C Numbers k such that A053669(k) is in A002144.

%C The asymptotic density of this sequence is Sum_{p prime, p == 1 (mod 4)} ((p-1)/(Product_{q prime, q <= p} q)) = 0.1337642792... . - _Amiram Eldar_, Jul 25 2022

%e The smallest prime that does not divide 6 = 2*3, is 5, which is of the form 4m+1, therefore 6 is included in this sequence.

%t f[n_] := Module[{p = 2}, While[Divisible[n, p], p = NextPrime[p]]; p]; Select[Range[500], Mod[f[#], 4] == 1 &] (* _Amiram Eldar_, Jul 25 2022 *)

%o (PARI)

%o A053669(n) = forprime(p=2, , if(n%p, return(p))); \\ From A053669

%o A353528(n) = (1==(A053669(n)%4));

%o isA353530(n) = A353528(n);

%Y This is not equal to A342051 \ A005408.

%Y Cf. A353531 for a complement among the even numbers.

%Y Cf. A002144, A053669, A353526, A353528 (characteristic function).

%K nonn

%O 1,1

%A _Antti Karttunen_, Apr 24 2022