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A005089
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Number of distinct primes = 1 mod 4 dividing n.
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9
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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, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 2, 0, 0, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 2, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 1
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OFFSET
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1,65
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COMMENTS
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a(n) = Sum(A079260(A027748(n,k)): k=1..A001221(n)); a(A004144(n)) = 0; a(A009003(n)) > 0. - Reinhard Zumkeller, Jan 07 2013
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LINKS
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Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
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FORMULA
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Additive with a(p^e) = 1 if p = 1 (mod 4), 0 otherwise.
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MATHEMATICA
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f[n_]:=Length@Select[If[n==1, {}, FactorInteger[n]], Mod[#[[1]], 4]==1&]; Table[f[n], {n, 102}] (* Ray Chandler, Dec 18 2011 *)
a[n_] := DivisorSum[n, Boole[PrimeQ[#] && Mod[#, 4] == 1]&]; Array[a, 100] (* Jean-François Alcover, Dec 01 2015 *)
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PROG
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(PARI) for(n=1, 100, print1(sumdiv(n, d, isprime(d)*if((d-1)%4, 0, 1)), ", "))
(Haskell)
a005089 = sum . map a079260 . a027748_row
-- Reinhard Zumkeller, Jan 07 2013
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CROSSREFS
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Cf. A001221, A005091, A005094.
Sequence in context: A320005 A325414 A216510 * A119395 A087476 A307505
Adjacent sequences: A005086 A005087 A005088 * A005090 A005091 A005092
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane.
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STATUS
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approved
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