A078910 Let r+i*s be the sum of the distinct first-quadrant Gaussian integers dividing n; sequence gives r values.

1, 4, 4, 10, 9, 16, 8, 22, 13, 37, 12, 40, 19, 32, 36, 46, 23, 52, 20, 93, 32, 48, 24, 88, 56, 77, 40, 80, 37, 148, 32, 94, 48, 95, 72, 130, 45, 80, 76, 205, 51, 128, 44, 120, 117, 96, 48, 184, 57, 231, 92, 193, 63, 160, 108, 176, 80, 151, 60, 372, 73, 128, 104, 190, 176

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.

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) = 10.
		

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. A000203, A078911, A078458, A078908, A078909, A078930.

Cf. A062327 for the number of first quadrant divisors of n.

Programs

Mathematica

Table[Re[Plus@@Divisors[n, GaussianIntegers -> True]], {n, 65}] (* Alonso del Arte, Jan 24 2012 *)

PARI

A078910(n,S=[])=sigma(n)+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

Formula

a(n) = A078911(n)+A000203(n). - Vladeta Jovovic, Jan 11 2003

Extensions

More terms from Vladeta Jovovic, Jan 11 2003