A268378 Numbers whose prime factorization includes at least one prime factor of form 4k+3 and any prime factor of the form 4k+1 has even multiplicity.

3, 6, 7, 9, 11, 12, 14, 18, 19, 21, 22, 23, 24, 27, 28, 31, 33, 36, 38, 42, 43, 44, 46, 47, 48, 49, 54, 56, 57, 59, 62, 63, 66, 67, 69, 71, 72, 75, 76, 77, 79, 81, 83, 84, 86, 88, 92, 93, 94, 96, 98, 99, 103, 107, 108, 112, 114, 118, 121, 124, 126, 127, 129, 131, 132, 133, 134, 138, 139, 141, 142, 144, 147, 150

Offset: 1

Author

Antti Karttunen, Feb 03 2016

Keywords

• nonn

Comments

Closed under multiplication.

Examples

			6 = 2*3 is included, as there is a prime factor of the form 4k+3 present.
75 = 3 * 5 * 5 is included, as there is a prime factor of the form 4k+3 present and the prime factor of the form 4k+1 (5) is present twice.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A065339, A267113.

Cf. A004431, A267099.

Subsequence of A268377.

Differs from A221264 for the first time at n=38, which here is a(38) = 75, a value missing from A221264.

Programs

Mathematica

Select[Range@ 150, AnyTrue[#, Mod[First@ #, 4] == 3 &] && NoneTrue[#, And[Mod[First@ #, 4] == 1, OddQ@ Last@ #] &] &@ FactorInteger@ # &] (* Michael De Vlieger, Feb 04 2016, Version 10 *)

PARI

isok(n) = {my(f = factor(n), nb3 = 0); for (i=1, #f~, if (((f[i,1] % 4) == 1) && (f[i,2] % 2), return (0)); if ((f[i,1] % 4) == 3, nb3++);); return (nb3);} \\ Michel Marcus, Feb 04 2016