|
|
A078908
|
|
Let r+i*s be the sum, with multiplicity, of the first-quadrant Gaussian primes dividing n; sequence gives r values (with a(1) = 0).
|
|
7
|
|
|
0, 2, 3, 4, 3, 5, 7, 6, 6, 5, 11, 7, 5, 9, 6, 8, 5, 8, 19, 7, 10, 13, 23, 9, 6, 7, 9, 11, 7, 8, 31, 10, 14, 7, 10, 10, 7, 21, 8, 9, 9, 12, 43, 15, 9, 25, 47, 11, 14, 8, 8, 9, 9, 11, 14, 13, 22, 9, 59, 10, 11, 33, 13, 12, 8, 16, 67, 9, 26, 12, 71, 12, 11, 9, 9, 23, 18, 10, 79, 11, 12, 11
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
A Gaussian integer z = x+iy is in the first quadrant if x > 0, y >= 0. Just one of the 4 associates z, -z, i*z, -i*z is in the first quadrant.
The sequence is fully additive.
|
|
LINKS
|
|
|
EXAMPLE
|
5 factors into the product of the primes 1+2*i, 1-2*i, but the first-quadrant associate of 1-2*i is i*(1-2*i) = 2+i, so r+i*s = 1+2*i + 2+i = 3+3*i. Therefore a(5) = 3.
|
|
MATHEMATICA
|
a[n_] := Module[{f = FactorInteger[n, GaussianIntegers->True]}, p = f[[;; , 1]]; e = f[[;; , 2]]; Re[Plus @@ ((If[Abs[#] == 1, 0, #]& /@ p) * e)]]; Array[a, 100] (* Amiram Eldar, Feb 28 2020 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|