|
Search: id:A100885
|
|
|
| A100885 |
|
Gaussian perfect numbers. Definition : GSigma(n)=m*n for some Gaussian integer m, where if n=Product p_i^r_i then GSigma(n)=Product (Sum p_i^s_i, 0<=s_i<=r_i). Sequence gives imaginary part of Gaussian perfect number. |
|
+0
2
|
| |
|
|
OFFSET
|
1,1
|
|
|
COMMENT
|
The following condition is necessary for defining "Sum" of Gaussian integers. If a Gaussian integer is of the form : r*e^(i*t), then 0<=t<Pi/2. GSigma(n) is a formal sum of divisors of n. Indeed, sometimes it gives a kind of difference of divisors of n.
|
|
EXAMPLE
|
GSigma((1+i)^7)=1+1+i+2+2+2*i+4+4+4*i+8+8+8*i=30+15*i
GSigma((1+i)*(2+i))=1+1+i+2+i+1+3i = 5+5i =(1+i)*(2+i)*(1+2i), so (1+i)*(2+i)=1+3i is a Gaussian perfect number.
|
|
CROSSREFS
|
Adjacent sequences: A100882 A100883 A100884 this_sequence A100886 A100887 A100888
Sequence in context: A007695 A011969 A003187 this_sequence A003186 A006826 A000214
|
|
KEYWORD
|
nonn,uned
|
|
AUTHOR
|
Yasutoshi Kohmoto (zbi74583(AT)boat.zero.ad.jp)
|
|
|
Search completed in 0.002 seconds
|
