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%I #39 Dec 22 2021 07:43:40
%S 0,0,0,0,1,0,0,0,0,1,0,0,1,0,1,0,1,0,0,1,0,0,0,0,2,1,0,0,1,1,0,0,0,1,
%T 1,0,1,0,1,1,1,0,0,0,1,0,0,0,0,2,1,1,1,0,1,0,0,1,0,1,1,0,0,0,2,0,0,1,
%U 0,1,0,0,1,1,2,0,0,1,0,1,0,1,0,0,2,0,1,0,1,1,1,0,0,0,1,0,1,0,0,2,1,1,0,1,1
%N Number of primes congruent to 1 modulo 4 dividing n (with multiplicity).
%D David A. Cox, "Primes of the Form x^2 + n y^2", Wiley, 1989, p. 61.
%H T. D. Noe, <a href="/A083025/b083025.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = A001222(n) - A007814(n) - A065339(n).
%p A083025 := proc(n)
%p a := 0 ;
%p for f in ifactors(n)[2] do
%p if op(1,f) mod 4 = 1 then
%p a := a+op(2,f) ;
%p end if;
%p end do:
%p a ;
%p end proc: # _R. J. Mathar_, Dec 16 2011
%t f[n_]:=Plus@@Last/@Select[If[n==1,{},FactorInteger[n]],Mod[#[[1]],4]==1&]; Table[f[n],{n,100}] (* _Ray Chandler_, Dec 18 2011 *)
%o (Haskell)
%o a083025 1 = 0
%o a083025 n = length [x | x <- a027746_row n, mod x 4 == 1]
%o -- _Reinhard Zumkeller_, Jan 10 2012
%o (PARI) A083025(n)=sum(i=1,#n=factor(n)~,if(n[1,i]%4==1,n[2,i])) \\ _M. F. Hasler_, Apr 16 2012
%Y First differs from A046080 at n=65.
%Y Cf. A001222, A007814, A027746, A065339 (== 3 (mod 4)).
%K nonn,easy,nice
%O 1,25
%A _Reinhard Zumkeller_, Oct 29 2001
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