cp's OEIS Frontend

A083025 Number of primes congruent to 1 modulo 4 dividing n (with multiplicity).

%I A083025 #46 Jan 27 2025 05:36:18
%S A083025 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 A083025 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 A083025 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 A083025 Number of primes congruent to 1 modulo 4 dividing n (with multiplicity).
%D A083025 David A. Cox, "Primes of the Form x^2 + n y^2", Wiley, 1989, p. 61.
%H A083025 T. D. Noe, <a href="/A083025/b083025.txt">Table of n, a(n) for n = 1..10000</a>
%F A083025 a(n) = A001222(n) - A007814(n) - A065339(n).
%F A083025 Totally additive with a(2) = 0, a(p) = 1 if p == 1 (mod 4), and a(p) = 0 if p == 3 (mod 4). - _Amiram Eldar_, Jun 17 2024
%p A083025 A083025 := proc(n)
%p A083025     a := 0 ;
%p A083025     for f in ifactors(n)[2] do
%p A083025         if op(1,f) mod 4 = 1 then
%p A083025             a := a+op(2,f) ;
%p A083025         end if;
%p A083025     end do:
%p A083025     a ;
%p A083025 end proc: # _R. J. Mathar_, Dec 16 2011
%t A083025 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 A083025 (Haskell)
%o A083025 a083025 1 = 0
%o A083025 a083025 n = length [x | x <- a027746_row n, mod x 4 == 1]
%o A083025 -- _Reinhard Zumkeller_, Jan 10 2012
%o A083025 (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 A083025 First differs from A046080 at n=65.
%Y A083025 Cf. A001222, A007814, A027746, A065339 (== 3 (mod 4)), A378879 (=2,3 (mod 4)), A005089 (without multiplicity).
%K A083025 nonn,easy,nice
%O A083025 1,25
%A A083025 _Reinhard Zumkeller_, Oct 29 2001