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A083025 Number of primes congruent to 1 modulo 4 dividing n (with multiplicity). 38
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,25
REFERENCES
David A. Cox, "Primes of the Form x^2 + n y^2", Wiley, 1989, p. 61.
LINKS
FORMULA
a(n) = A001222(n) - A007814(n) - A065339(n).
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
KEYWORD
nonn,easy,nice
AUTHOR
Reinhard Zumkeller, Oct 29 2001
STATUS
approved

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Last modified March 28 08:22 EDT 2024. Contains 371236 sequences. (Running on oeis4.)