OFFSET
1,9
COMMENTS
a(n) = {number of primes of the form 4k+1 dividing n} minus {number of primes of the form 4k+3 dividing n}, both counted with multiplicity. - Antti Karttunen, Feb 03 2016, after the formula.
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
FORMULA
Other identities. For all n >= 1:
a(A267099(n)) = -a(n). - Antti Karttunen, Feb 03 2016
Totally additive with a(2) = 0, a(p) = 1 if p == 1 (mod 4), and a(p) = -1 if p == 3 (mod 4). - Amiram Eldar, Jun 17 2024
EXAMPLE
a(55) = a(5*11) = (2 - 5 mod 4)+(2 - 11 mod 4) = (2-1)+(2-3) = (1)+(-1) = 0.
MAPLE
f:= proc(n) local t;
add(t[2]*(2-(t[1] mod 4)), t=ifactors(n)[2])
end proc:
map(f, [$1..100]); # Robert Israel, Feb 05 2016
MATHEMATICA
f[n_]:=Plus@@((2-Mod[#[[1]], 4])*#[[2]]&/@If[n==1, {}, FactorInteger[n]]); Table[f[n], {n, 100}] (* Ray Chandler, Dec 20 2011 *)
PROG
(Haskell)
a079635 1 = 0
a079635 n = sum $ map ((2 - ) . (`mod` 4)) $ a027746_row n
-- Reinhard Zumkeller, Jan 10 2012
CROSSREFS
KEYWORD
sign
AUTHOR
Reinhard Zumkeller, Jan 30 2003
EXTENSIONS
Edited by Ray Chandler, Dec 20 2011
STATUS
approved