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%I #29 Jun 28 2022 15:28:55
%S 5,10,13,17,20,25,26,29,34,37,40,41,50,52,53,58,61,65,68,73,74,75,80,
%T 82,85,89,97,100,101,104,106,109,113,116,122,125,130,136,137,145,146,
%U 148,149,150,157,160,164,169,170,173,175,178,181,185,193,194,195,197,200,202,205,208,212,218,221
%N Numbers having more prime factors of the form 4*k+1 than of the form 4*k+3, when counted with multiplicity.
%C Numbers n for which A083025(n) > A065339(n) or equally, for which A079635(n) > 0.
%C Closed under multiplication.
%H Antti Karttunen, <a href="/A268379/b268379.txt">Table of n, a(n) for n = 1..10000</a>
%e 75 = 3*5*5 is included as there are more prime factors of the form 4k+1 (here two 5's) than of the form 4k+3 (here just one 3).
%t Rest@ Position[Array[Map[Length, {Select[#, Mod[#, 4] == 1 &], Select[#, Mod[#, 4] == 3 &]}] &@ Flatten@ Apply[Table[#1, {#2}] &, FactorInteger@ #, 1] &, {221}], {a_, b_} /; a > b] // Flatten (* _Michael De Vlieger_, Feb 05 2016 *)
%o (Scheme, with _Antti Karttunen_'s IntSeq-library)
%o (define A268379 (MATCHING-POS 1 1 (lambda (n) (> (A083025 n) (A065339 n)))))
%o (define A268379 (MATCHING-POS 1 1 (COMPOSE positive? A079635)))
%o (PARI) isok(n) = {my(f = factor(n), nb1 = 0, nb3 = 0); for (i=1, #f~, m = f[i,1] % 4; if (m == 1, nb1 += f[i,2], if (m == 3, nb3 += f[i,2]));); return (nb1 > nb3);} \\ _Michel Marcus_, Feb 04 2016
%o (Python)
%o from itertools import count, islice
%o from sympy import factorint
%o def A268379_gen(): # generator of terms
%o return filter(lambda n:sum((f:=factorint(n)).values())-f.get(2,0) < 2*sum(f[p] for p in f if p & 3 == 1),count(1))
%o A268379_list = list(islice(A268379_gen(),30)) # _Chai Wah Wu_, Jun 28 2022
%Y Cf. A065339, A079635, A083025.
%Y Cf. also A001481, A072202, A268380.
%Y Subsequence of A268381.
%Y Differs from A221265 for the first time at n=22, as here a(22) = 75, a value missing from A221265.
%K nonn
%O 1,1
%A _Antti Karttunen_, Feb 03 2016
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