A078930 Let r+i*s be the sum of the distinct first-quadrant Gaussian integers dividing n; sequence gives r+s values.

1, 5, 4, 13, 12, 20, 8, 29, 13, 56, 12, 52, 24, 40, 48, 61, 28, 65, 20, 144, 32, 60, 24, 116, 81, 112, 40, 104, 44, 224, 32, 125, 48, 136, 96, 169, 52, 100, 96, 320, 60, 160, 44, 156, 156, 120, 48, 244, 57, 369, 112, 288, 72, 200, 144, 232, 80, 212, 60, 576, 84, 160, 104

Offset: 1

Author

Vladeta Jovovic, Jan 11 2003

Keywords

• nonn

Comments

A078910(n)-A078911(n) = A000203(n).

Also equal to the sum of all divisors of n (in Z[i]) having positive real part. - M. F. Hasler, Nov 22 2007

Links

• M. F. Hasler, Table of n, a(n) for n = 1..1000.
• Project Euler, Problem 153: Investigating Gaussian Integers.

Programs

PARI

A078930(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) = A078910(n)+A078911(n).

a(n) = A000203(n)+2*A078911(n). - M. F. Hasler, Nov 22 2007