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A005091 Number of distinct primes = 3 mod 4 dividing n. 10
0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 2, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 2, 0, 1, 1, 0, 1, 1, 0, 0, 2, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 2, 0, 1, 1, 0, 1, 2, 0, 0, 2, 1, 0, 2, 1, 1, 1, 0, 0, 1, 1, 2, 1, 1, 0, 1, 0, 1, 2, 0, 1, 1, 1, 0, 1, 1, 1, 2, 1, 1, 1, 0, 1, 2, 0, 0, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,21

COMMENTS

a(n) = Sum_{k=1..A001221(n)} A079261(A027748(n,k)); a(A072437(n)) = 0; a(A187811(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 = 3 (mod 4), 0 otherwise.

a(n) = Sum_{p|n} (binomial(p,3) mod 2), where p is a prime. - Ridouane Oudra, Nov 19 2019

MAPLE

with(numtheory): seq(add(binomial(p, 3) mod 2, p in factorset(n)), n=1..100); # Ridouane Oudra, Nov 19 2019

MATHEMATICA

f[n_]:=Length@Select[If[n==1, {}, FactorInteger[n]], Mod[#[[1]], 4]==3&]; Table[f[n], {n, 102}] (* Ray Chandler, Dec 18 2011 *)

PROG

(PARI) for(n=1, 100, print1(sumdiv(n, d, isprime(d)*if((d-3)%4, 0, 1)), ", "))

(Haskell)

a005091 = sum . map a079261 . a027748_row

-- Reinhard Zumkeller, Jan 07 2013

(MAGMA) [0] cat [#[p:p in PrimeDivisors(n)| p mod 4 eq 3]: n in [2..100]]; // Marius A. Burtea, Nov 19 2019

(MAGMA) [0] cat [&+[Binomial(p, 3) mod 2:p in PrimeDivisors(n)]:n in [2..100]]; // Marius A. Burtea, Nov 19 2019

CROSSREFS

Cf. A001221, A005089, A005094.

Sequence in context: A277778 A255319 A214088 * A276516 A253638 A086831

Adjacent sequences:  A005088 A005089 A005090 * A005092 A005093 A005094

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified December 7 17:41 EST 2019. Contains 329847 sequences. (Running on oeis4.)