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A005089 Number of distinct primes = 1 mod 4 dividing n. 9
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

COMMENTS

a(n) = Sum(A079260(A027748(n,k)): k=1..A001221(n)); a(A004144(n)) = 0; a(A009003(n)) > 0. - Reinhard Zumkeller, Jan 07 2013

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

FORMULA

Additive with a(p^e) = 1 if p = 1 (mod 4), 0 otherwise.

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-Fran├žois 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

CROSSREFS

Cf. A001221, A005091, A005094.

Sequence in context: A320005 A325414 A216510 * A119395 A087476 A307505

Adjacent sequences:  A005086 A005087 A005088 * A005090 A005091 A005092

KEYWORD

nonn

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified December 8 02:05 EST 2019. Contains 329850 sequences. (Running on oeis4.)