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Numbers having fewer distinct prime factors of form 4*k+1 than of 4*k+3.
6

%I #19 Jul 13 2024 07:05:00

%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 48,49,54,56,57,59,62,63,66,67,69,71,72,76,77,79,81,83,84,86,88,92,93,

%U 94,96,98,99,103,105,107,108,112,114,118,121,124,126,127,129

%N Numbers having fewer distinct prime factors of form 4*k+1 than of 4*k+3.

%C A005089(a(n)) < A005091(a(n)); A005094(a(n)) < 0.

%H Reinhard Zumkeller, <a href="/A221264/b221264.txt">Table of n, a(n) for n = 1..10000</a>

%o (Haskell)

%o a221264 n = a221264_list !! (n-1)

%o a221264_list = filter ((< 0) . a005094) [1..]

%o (PARI) is_A221264(n)={#(n=vecsort(factor(n>>valuation(n,2))[,1]%4))&&n[(1+#n)\2]==3} \\ _M. F. Hasler_, Dec 17 2014

%Y Cf. A005089, A005091, A005094, A078613, A221265.

%K nonn,easy

%O 1,1

%A _Reinhard Zumkeller_, Jan 07 2013