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A100884
Real parts of multiperfect Gaussian numbers z, sorted with respect to |z| and Re(z).
8
1, 1, 6, 5, 10, 12, 60, 72, 28, 100, 108, 120, 204, 300, 263, 140, 526, 912, 150, 720, 1470, 1520, 1200, 1704, 672, 600, 4560, 4828, 3600, 5584, 5880, 4680, 6312, 6240, 1800, 2160, 14484, 17640, 8984, 72824, 62400
OFFSET
1,3
COMMENTS
Sort the Gaussian integers z in the first quadrant according to increasing modulus |z|, and within the same modulus according to increasing Re(z): 1, 1+i, 2, 1+2i, 2+i, 2+2i, 3, 1+3i, 3+i, 2+3i, 3+2i,...
If z divides the value of sigma(z), defined in A103228, i.e., if sigma(z)=z*m with m some Gaussian integer (m not necessarily in the first quadrant), add Re(z) to the sequence.
EXAMPLE
For z = 1, sigma(z) = 1 and m = sigma(z)/z = 1, which adds 1 to the sequence.
For z = 1+3i, sigma(z) = 5+5i and m = sigma(z)/z = 2-i, which adds 1 to the sequence.
For z = 6+2i, sigma(z) = -10+10i and m = sigma(z)/z = -1+2i, which adds 6 to the sequence.
For z = 5+5i, sigma(z) = 20i and m = sigma(z)/ z= 2+2i, which adds 5 to the sequence.
For z = (1+i)^7 = 8-8i, the divisors are 1, 1+i, (1+i)^2 = 2i, (1+i)^3 = -2+2i, (1+i)^4 = -4, (1+i)^5= -4-4i, (1+i)^6 = -8i, (1+i)^7 = 8-8i. So sigma(z) is 1 +1+i +2i -2+2i -4 -4-4i -8i +8-8i = -15i and sigma(z)/z is m = -15i/(8-8i) which is not a Gaussian integer, so Re(z)=8 is NOT added to the sequence.
CROSSREFS
KEYWORD
nonn,more
EXTENSIONS
Entirely rewritten, including the a(n), by R. J. Mathar, Mar 12 2010
a(10)-a(41) from Amiram Eldar, Feb 10 2020
STATUS
approved