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

Author

N. J. A. Sloane, Jan 11 2003

Keywords

• nonn
• easy

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

Examples

			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.
		

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

Crossrefs

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

Programs

Mathematica

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

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

Extensions

More terms from Vladeta Jovovic, Jan 11 2003