OFFSET
1,21
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 = 3 (mod 4), 0 otherwise.
From Reinhard Zumkeller, Jan 07 2013: (Start)
a(A072437(n)) = 0.
a(A187811(n)) > 0. (End)
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
(Python)
from sympy import primefactors
def A005091(n): return sum(1 for p in primefactors(n) if p&3==3) # Chai Wah Wu, Jul 07 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved