A078930 - OEIS

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

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OFFSET

1,2

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.

FORMULA

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

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

PROG

(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

CROSSREFS

Sequence in context: A226555 A147685 A353151 * A329162 A344817 A094414

Adjacent sequences: A078927 A078928 A078929 * A078931 A078932 A078933

KEYWORD

nonn

AUTHOR

Vladeta Jovovic, Jan 11 2003

STATUS

approved