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A268380 Numbers having fewer prime factors of the form 4*k+1 than of the form 4*k+3, when counted with multiplicity. 4

%I

%S 3,6,7,9,11,12,14,18,19,21,22,23,24,27,28,31,33,36,38,42,43,44,45,46,

%T 47,48,49,54,56,57,59,62,63,66,67,69,71,72,76,77,79,81,83,84,86,88,90,

%U 92,93,94,96,98,99,103,105,107,108,112,114,117,118,121,124,126,127,129,131,132,133,134,135,138,139,141

%N Numbers having fewer 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="/A268380/b268380.txt">Table of n, a(n) for n = 1..10000</a>

%e 45 = 3*3*5 is included as there are more prime factors of the form 4k+3 (here two 3's) than prime factors of the form 4k+1 (here just one 5).

%t Position[Array[Map[Length, {Select[#, Mod[#, 4] == 1 &], Select[#, Mod[#, 4] == 3 &]}] &@ Flatten@ Apply[Table[#1, {#2}] &, FactorInteger@ #, 1] &, {141}], {a_, b_} /; a < b] // Flatten (* _Michael De Vlieger_, Feb 05 2016 *)

%o (Scheme, with _Antti Karttunen_'s IntSeq-library)

%o (define A268380 (MATCHING-POS 1 1 (lambda (n) (< (A083025 n) (A065339 n)))))

%o (PARI) isok(n) = {my(f = factor(n)); sum(k=1, #f~, ((f[k,1] % 4)==1)*f[k,2]) < sum(k=1, #f~, ((f[k,1] % 4)==3)*f[k,2]);} \\ _Michel Marcus_, Feb 05 2016

%Y Complement: A268381.

%Y Cf. A079635, A065339, A083025.

%Y Cf. also A072202, A268379.

%Y Differs from A221264 for the first time at n=23, where a(23) = 45, a value missing from A221264.

%K nonn

%O 1,1

%A _Antti Karttunen_, Feb 05 2016

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Last modified May 22 21:17 EDT 2019. Contains 323504 sequences. (Running on oeis4.)