The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A100884

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A100884

Real parts of multiperfect Gaussian numbers z, sorted with respect to |z| and Re(z).
(history; published version)

#19 by Michel Marcus at Sat Aug 27 04:05:16 EDT 2022

STATUS

reviewed

approved

#18 by Joerg Arndt at Sat Aug 27 03:44:43 EDT 2022

STATUS

proposed

reviewed

#17 by Jon E. Schoenfield at Sat Aug 27 02:50:04 EDT 2022

STATUS

editing

proposed

#16 by Jon E. Schoenfield at Sat Aug 27 02:50:02 EDT 2022

COMMENTS

If z divides the value of sigma(z), defined in A103228, ie, 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.

STATUS

approved

editing

#15 by Amiram Eldar at Mon Feb 10 09:02:01 EST 2020

STATUS

editing

approved

#14 by Amiram Eldar at Mon Feb 10 08:52:22 EST 2020

DATA

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

EXTENSIONS

a(10)-a(3441) from Amiram Eldar, Feb 10 2020

STATUS

approved

editing

#13 by Joerg Arndt at Mon Feb 10 05:20:36 EST 2020

STATUS

reviewed

approved

#12 by Michel Marcus at Mon Feb 10 03:34:37 EST 2020

STATUS

proposed

reviewed

#11 by Amiram Eldar at Mon Feb 10 03:29:14 EST 2020

STATUS

editing

proposed

#10 by Amiram Eldar at Mon Feb 10 02:43:41 EST 2020

DATA

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

EXTENSIONS

a(10)-a(34) from Amiram Eldar, Feb 10 2020

STATUS

approved

editing