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

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, 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, 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

Offset

1,25

References

David A. Cox, "Primes of the Form x^2 + n y^2", Wiley, 1989, p. 61.

Links

T. D. Noe, Table of n, a(n) for n = 1..10000

Formula

a(n) = A001222(n) - A007814(n) - A065339(n).

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

Maple

A083025 := proc(n)
    a := 0 ;
    for f in ifactors(n)[2] do
        if op(1, f) mod 4 = 1 then
            a := a+op(2, f) ;
        end if;
    end do:
    a ;
end proc: # R. J. Mathar, Dec 16 2011

Mathematica

f[n_]:=Plus@@Last/@Select[If[n==1, {}, FactorInteger[n]], Mod[#[[1]], 4]==1&]; Table[f[n], {n, 100}] (* Ray Chandler, Dec 18 2011 *)

Prog

(Haskell)
a083025 1 = 0
a083025 n = length [x | x <- a027746_row n, mod x 4 == 1]
-- Reinhard Zumkeller, Jan 10 2012
(PARI) A083025(n)=sum(i=1, #n=factor(n)~, if(n[1, i]%4==1, n[2, i]))  \\ M. F. Hasler, Apr 16 2012

Crossrefs

First differs from A046080 at n=65.

Cf. A001222, A007814, A027746, A065339 (== 3 (mod 4)).

Sequence in context: A015964 A088950 A267113 * A046080 A170967 A035227

Adjacent sequences: A083022 A083023 A083024 * A083026 A083027 A083028

Keyword

nonn,easy,nice

Author

Reinhard Zumkeller, Oct 29 2001

Status

approved