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A353530 Numbers k such that the smallest prime that does not divide them is of the form 4m+1. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
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
LINKS
EXAMPLE
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.
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 *)
PROG
(PARI)
A053669(n) = forprime(p=2, , if(n%p, return(p))); \\ From A053669
A353528(n) = (1==(A053669(n)%4));
isA353530(n) = A353528(n);
CROSSREFS
This is not equal to A342051 \ A005408.
Cf. A353531 for a complement among the even numbers.
Cf. A002144, A053669, A353526, A353528 (characteristic function).
Sequence in context: A189781 A182302 A358757 * A244193 A329878 A215142
KEYWORD
nonn
AUTHOR
Antti Karttunen, Apr 24 2022
STATUS
approved

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Last modified July 24 12:40 EDT 2024. Contains 374583 sequences. (Running on oeis4.)