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A072202 Same numbers of prime factors of forms 4*k+1 and 4*k+3, counted with multiplicity.

%I A072202 #31 Feb 05 2016 20:39:46
%S A072202 1,2,4,8,15,16,30,32,35,39,51,55,60,64,70,78,87,91,95,102,110,111,115,
%T A072202 119,120,123,128,140,143,155,156,159,174,182,183,187,190,203,204,215,
%U A072202 219,220,222,225,230,235,238,240,246,247,256,259,267,280,286,287,291
%N A072202 Same numbers of prime factors of forms 4*k+1 and 4*k+3, counted with multiplicity.
%C A072202 Equivalently, numbers n such that A083025(n) = A065339(n), indices of zeros in A079635.
%C A072202 Closed under multiplication.
%C A072202 Closed with respect to permutation A267099. - _Antti Karttunen_, Feb 03 2016
%H A072202 Reinhard Zumkeller, <a href="/A072202/b072202.txt">Table of n, a(n) for n = 1..10000</a>
%e A072202 825 = 3*5*5*11 = [(4*0+3)*(4*2+3)]*[(4*1+1)*(4*1+1)], therefore 825 is a term.
%t A072202 f[n_]:=Plus@@Last/@Select[If[==1,{},FactorInteger[n]],Mod[#[[1]],4]==1&]; Table[f[n],{n,100}] (* _Ray Chandler_, Dec 18 2011 *)
%o A072202 (Haskell)
%o A072202 a072202 n = a072202_list !! (n-1)
%o A072202 a072202_list = [x | x <- [1..], a083025 x == a065339 x]
%o A072202 -- _Reinhard Zumkeller_, Jan 10 2012
%o A072202 (Scheme) (define A072202 (ZERO-POS 1 1 A079635)) ;; [requires also my IntSeq-library] - _Antti Karttunen_, Feb 03 2016
%o A072202 (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 A072202 Cf. A002144, A002145, A202237 (odd elements), A079635, A065339, A083025, A267099.
%Y A072202 Primitive elements are {2} U A080774. - _Franklin T. Adams-Watters_, Dec 16 2011.
%Y A072202 Subsequence of A078613 and of A268381.
%K A072202 nonn
%O A072202 1,2
%A A072202 _Reinhard Zumkeller_, Jul 03 2002