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Numbers with no prime factors of form 4*k+3.
12

%I #27 Nov 12 2013 18:15:10

%S 1,2,4,5,8,10,13,16,17,20,25,26,29,32,34,37,40,41,50,52,53,58,61,64,

%T 65,68,73,74,80,82,85,89,97,100,101,104,106,109,113,116,122,125,128,

%U 130,136,137,145,146,148,149,157,160,164,169,170,173,178,181,185,193,194

%N Numbers with no prime factors of form 4*k+3.

%C m is a term iff A072436(m) = m.

%C These numbers have density zero (Pollack).

%C A005091(a(n)) = 0. - _Reinhard Zumkeller_, Jan 07 2013

%H Reinhard Zumkeller, <a href="/A072437/b072437.txt">Table of n, a(n) for n = 1..10000</a>

%H P. Pollack, <a href="http://alpha01.dm.unito.it/personalpages/cerruti/ac/notes.pdf">Analytic and Combinatorial Number Theory</a> Course Notes, p. 119. <a href="http://www.math.dartmouth.edu/~ppollack/notes.pdf">alternate link</a>

%F n>0 such that A001842(n)=0. - _Benoit Cloitre_, Apr 24 2003

%t npfQ[n_]:=Count[Transpose[FactorInteger[n]][[1]],_?(Mod[#,4]==3&)]==0; Select[Range[200],npfQ] (* _Harvey P. Dale_, Nov 12 2013 *)

%o (PARI) is(n)=n==1||vecmax(factor(n)[,1]%4)<3 \\ _Charles R Greathouse IV_, Apr 16 2012

%o (Haskell)

%o import Data.List (elemIndices)

%o a072437 n = a072437_list !! (n-1)

%o a072437_list = map (+ 1) $ elemIndices 0 a005091_list

%o -- _Reinhard Zumkeller_, Jan 07 2013

%Y Cf. A004144, A002144, A002145.

%Y A097706(a(n)) = 1.

%Y Cf. A187811 (complement).

%K nonn

%O 1,2

%A _Reinhard Zumkeller_, Jun 17 2002