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A078909 Let r+i*s be the sum, with multiplicity, of the first-quadrant Gaussian primes dividing n; sequence gives s values. 5
0, 2, 0, 4, 3, 2, 0, 6, 0, 5, 0, 4, 5, 2, 3, 8, 5, 2, 0, 7, 0, 2, 0, 6, 6, 7, 0, 4, 7, 5, 0, 10, 0, 7, 3, 4, 7, 2, 5, 9, 9, 2, 0, 4, 3, 2, 0, 8, 0, 8, 5, 9, 9, 2, 3, 6, 0, 9, 0, 7, 11, 2, 0, 12, 8, 2, 0, 9, 0, 5, 0, 6, 11, 9, 6, 4, 0, 7, 0, 11, 0, 11, 0, 4, 8, 2, 7, 6, 13, 5, 5, 4, 0, 2, 3, 10, 13, 2, 0 (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

Table of n, a(n) for n=1..99.

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.

CROSSREFS

Cf. A078458, A078908, A078910, A078911, A080088, A080089.

Sequence in context: A145382 A192423 A265584 * A067458 A088330 A324471

Adjacent sequences:  A078906 A078907 A078908 * A078910 A078911 A078912

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Jan 11 2003

EXTENSIONS

More terms and further information from Vladeta Jovovic, Jan 27 2003

STATUS

approved

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Last modified March 21 07:23 EDT 2019. Contains 321367 sequences. (Running on oeis4.)