|
%I #14 Feb 05 2016 20:48:41
%S 3,6,7,9,11,12,14,18,19,21,22,23,24,27,28,31,33,36,38,42,43,44,46,47,
%T 48,49,54,56,57,59,62,63,66,67,69,71,72,75,76,77,79,81,83,84,86,88,92,
%U 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
%N 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.
%C Closed under multiplication.
%H Antti Karttunen, <a href="/A268378/b268378.txt">Table of n, a(n) for n = 1..10000</a>
%e 6 = 2*3 is included, as there is a prime factor of the form 4k+3 present.
%e 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.
%t 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 *)
%o (Scheme, with _Antti Karttunen_'s IntSeq-library)
%o (define A268378 (MATCHING-POS 1 1 (lambda (n) (and (even? (A267113 n)) (not (zero? (A065339 n)))))))
%o (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
%Y Cf. A065339, A267113.
%Y Cf. A004431, A267099.
%Y Subsequence of A268377.
%Y Differs from A221264 for the first time at n=38, which here is a(38) = 75, a value missing from A221264.
%K nonn
%O 1,1
%A _Antti Karttunen_, Feb 03 2016
|
