A078911 Let r+i*s be the sum of the distinct first-quadrant Gaussian integers dividing n; sequence gives s values.

0, 1, 0, 3, 3, 4, 0, 7, 0, 19, 0, 12, 5, 8, 12, 15, 5, 13, 0, 51, 0, 12, 0, 28, 25, 35, 0, 24, 7, 76, 0, 31, 0, 41, 24, 39, 7, 20, 20, 115, 9, 32, 0, 36, 39, 24, 0, 60, 0, 138, 20, 95, 9, 40, 36, 56, 0, 61, 0, 204, 11, 32, 0, 63, 92, 48, 0, 113, 0, 152, 0, 91, 11, 71, 100, 60, 0, 140

Offset

1,4

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.

a(A004614(n)) = 0; a(n) = A078910(n)-A000203(n). - Vladeta Jovovic, Jan 11 2003

Links

M. F. Hasler, Table of n, a(n) for n = 1..1000.

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

Index entries for Gaussian integers and primes

Example

The distinct first-quadrant divisors of 4 are 1, 1+i, 2, 2+2*i, 4, with sum 10+3*i, so a(4) = 3.

Mathematica

Table[Im[Plus@@Divisors[n, GaussianIntegers -> True]], {n, 65}] (* Alonso del Arte, Jan 24 2012; typo fixed by Virgile Andreani, Jul 10 2016 *)

Prog

(PARI) A078911(n, S=[])=sumdiv(n*I, d, if(real(d)&imag(d)&!setsearch(S, d=vecsort(abs([real(d), imag(d)]))), S=setunion(S, [d]); (d[1]+d[2])>>(d[1]==d[2]))) \\ M. F. Hasler, Nov 22 2007

Crossrefs

Cf. A078910, A078458, A078908, A078909, A078930.

Sequence in context: A117032 A243823 A281141 * A353417 A082899 A249491

Adjacent sequences: A078908 A078909 A078910 * A078912 A078913 A078914

Keyword

nonn,easy

Author

N. J. A. Sloane, Jan 11 2003

Extensions

More terms from Vladeta Jovovic, Jan 11 2003

Status

approved