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 A005089 Number of distinct primes == 1 (mod 4) dividing n. 10
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,65 LINKS Reinhard Zumkeller, Table of n, a(n) for n = 1..10000 Étienne Fouvry and Peter Koymans, On Dirichlet biquadratic fields, arXiv:2001.05350 [math.NT], 2020. FORMULA Additive with a(p^e) = 1 if p == 1 (mod 4), 0 otherwise. From Reinhard Zumkeller, Jan 07 2013: (Start) a(n) = Sum_{k=1..A001221(n)} A079260(A027748(n,k)). a(A004144(n)) = 0. a(A009003(n)) > 0. (End) MAPLE A005089 := proc(n) local a, pe; a := 0 ; for pe in ifactors(n)[2] do if modp(op(1, pe), 4) =1 then a := a+1 ; end if; end do: a ; end proc: seq(A005089(n), n=1..100) ; # R. J. Mathar, Jul 22 2021 MATHEMATICA 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 *) PROG (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 (Magma) [#[p:p in PrimeDivisors(n)|p mod 4 eq 1]: n in [1..100]]; // Marius A. Burtea, Jan 16 2020 CROSSREFS Cf. A001221, A005091, A005094. Cf. A079260, A027748, A004144, A009003. Sequence in context: A320005 A325414 A216510 * A364127 A340999 A119395 Adjacent sequences: A005086 A005087 A005088 * A005090 A005091 A005092 KEYWORD nonn AUTHOR N. J. A. Sloane STATUS approved

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Last modified May 18 09:54 EDT 2024. Contains 372620 sequences. (Running on oeis4.)