cp's OEIS Frontend

A072437 Numbers with no prime factors of form 4*k+3.

%I A072437 #31 Jan 28 2025 08:16:52
%S A072437 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 A072437 65,68,73,74,80,82,85,89,97,100,101,104,106,109,113,116,122,125,128,
%U A072437 130,136,137,145,146,148,149,157,160,164,169,170,173,178,181,185,193,194
%N A072437 Numbers with no prime factors of form 4*k+3.
%C A072437 m is a term iff A072436(m) = m.
%C A072437 These numbers have density zero (Pollack).
%H A072437 Reinhard Zumkeller, <a href="/A072437/b072437.txt">Table of n, a(n) for n = 1..10000</a>
%H A072437 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 A072437 n>0 such that A001842(n)=0. - _Benoit Cloitre_, Apr 24 2003
%F A072437 A005091(a(n)) = 0. - _Reinhard Zumkeller_, Jan 07 2013
%F A072437 A065339(a(n)) = 0 . - _R. J. Mathar_, Jan 28 2025
%t A072437 npfQ[n_]:=Count[Transpose[FactorInteger[n]][[1]],_?(Mod[#,4]==3&)]==0; Select[Range[200],npfQ] (* _Harvey P. Dale_, Nov 12 2013 *)
%o A072437 (PARI) is(n)=n==1||vecmax(factor(n)[,1]%4)<3 \\ _Charles R Greathouse IV_, Apr 16 2012
%o A072437 (Haskell)
%o A072437 import Data.List (elemIndices)
%o A072437 a072437 n = a072437_list !! (n-1)
%o A072437 a072437_list = map (+ 1) $ elemIndices 0 a005091_list
%o A072437 -- _Reinhard Zumkeller_, Jan 07 2013
%Y A072437 Cf. A004144, A002144, A002145, A004613 (odd terms).
%Y A072437 A097706(a(n)) = 1.
%Y A072437 Cf. A187811 (complement).
%K A072437 nonn
%O A072437 1,2
%A A072437 _Reinhard Zumkeller_, Jun 17 2002