A353530 Numbers k such that the smallest prime that does not divide them is of the form 4m+1.

6, 12, 18, 24, 36, 42, 48, 54, 66, 72, 78, 84, 96, 102, 108, 114, 126, 132, 138, 144, 156, 162, 168, 174, 186, 192, 198, 204, 216, 222, 228, 234, 246, 252, 258, 264, 276, 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

Offset: 1

Author

Antti Karttunen, Apr 24 2022

Keywords

• nonn

Comments

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

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

Examples

			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.
		

Crossrefs

This is not equal to A342051 \ A005408.

Cf. A353531 for a complement among the even numbers.

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

Programs

Mathematica

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 *)

PARI

A053669(n) = forprime(p=2, , if(n%p, return(p))); \\ From A053669
A353528(n) = (1==(A053669(n)%4));
isA353530(n) = A353528(n);