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%I #13 Feb 05 2016 20:48:30
%S 1,2,3,4,6,7,8,9,11,12,14,16,18,19,21,22,23,24,25,27,28,31,32,33,36,
%T 38,42,43,44,46,47,48,49,50,54,56,57,59,62,63,64,66,67,69,71,72,75,76,
%U 77,79,81,83,84,86,88,92,93,94,96,98,99,100,103,107,108,112,114,118,121,124,126,127,128,129,131,132,133
%N Numbers n such that any prime factor of the form 4k+1 has even multiplicity.
%C Closed under multiplication.
%H Antti Karttunen, <a href="/A268377/b268377.txt">Table of n, a(n) for n = 1..10000</a>
%e Neither 5 or 10 (= 2*5) are included, because the prime factor 5 (of the form 4k+1) occurs just once.
%e 6 = 2*3 is present, as there are no prime factors of 4k+1 present at all, and zero is an even number.
%e Also 25 (5*5) and 50 (2*5*5) and 75 (3*5*5) and 625 (5*5*5*5) are included, because in all of them, the prime factor 5 (of the form 4k+1) occurs an even number of times.
%t {1}~Join~Select[Range@ 140, NoneTrue[FactorInteger@ #, And[Mod[First@ #, 4] == 1, OddQ@ Last@ #] &] &] (* _Michael De Vlieger_, Feb 04 2016, Version 10 *)
%o (Scheme) (define A268377 (MATCHING-POS 1 1 (COMPOSE even? A267113)))
%o (PARI) isok(n) = {my(f = factor(n)); for (i=1, #f~, if (((f[i,1] % 4) == 1) && (f[i,2] % 2), return (0));); return (1);} \\ _Michel Marcus_, Feb 04 2016
%Y Cf. A267113.
%Y Cf. A268378 (a subsequence).
%Y Cf. A001481, A267099.
%K nonn
%O 1,2
%A _Antti Karttunen_, Feb 03 2016
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