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).

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

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

Amiram Eldar, Table of n, a(n) for n = 1..10000

Michael Somos, PARI program for finding prime decomposition of Gaussian integers

Index entries for Gaussian integers and primes

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

Cf. A078458, A078909, A078910, A078911, A080088, A080089.

Sequence in context: A336855 A329895 A342552 * A159797 A152920 A361442

Adjacent sequences: A078905 A078906 A078907 * A078909 A078910 A078911

Keyword

nonn,easy

Author

N. J. A. Sloane, Jan 11 2003

Extensions

More terms and information from Vladeta Jovovic, Jan 27 2003

Status

approved