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A083025
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Number of primes congruent to 1 modulo 4 dividing n (with multiplicity).
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39
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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
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OFFSET
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1,25
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REFERENCES
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David A. Cox, "Primes of the Form x^2 + n y^2", Wiley, 1989, p. 61.
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LINKS
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T. D. Noe, Table of n, a(n) for n = 1..10000
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FORMULA
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a(n) = A001222(n) - A007814(n) - A065339(n).
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MAPLE
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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
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MATHEMATICA
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f[n_]:=Plus@@Last/@Select[If[n==1, {}, FactorInteger[n]], Mod[#[[1]], 4]==1&]; Table[f[n], {n, 100}] (* Ray Chandler, Dec 18 2011 *)
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PROG
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(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
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CROSSREFS
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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
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KEYWORD
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nonn,easy,nice
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AUTHOR
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Reinhard Zumkeller, Oct 29 2001
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STATUS
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approved
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