|
| |
|
|
A066239
|
|
The floor(1.001*x)-perfect numbers, where f-perfect numbers for an arithmetical function f are defined in A066218.
|
|
0
| | |
|
|
|
OFFSET
| 1,1
|
|
|
COMMENTS
| The floor(n)-perfect numbers are the ordinary perfect numbers. The first three floor[1.001x]-perfect numbers are also ordinary perfect numbers and the first discrepancy comes at the fourth term, 32445 (the fourth perfect number is 8128). Consider other coefficients > 1 but < 1.001. There is some kind of continuity working here. The first discrepancies, if they exist, come at later and later terms as these coefficients are made closer to 1.
|
|
|
LINKS
| J. Pe, On a Generalization of Perfect Numbers, J. Rec. Math., 31(3) (2002-2003), 168-172.
|
|
|
EXAMPLE
| Let f(n) = floor(1.001*n). Then f(6) = 6 = 3+2+1 = f(3)+f(2)+f(1); so 6 is a term of the sequence.
|
|
|
MATHEMATICA
| f[x_] := Floor[1.001*x]; Select[ Range[1, 10^5], 2 * f[ # ] == Apply[ Plus, Map[ f, Divisors[ # ] ] ] & ]
|
|
|
CROSSREFS
| Sequence in context: A060286 A152953 A000396 * A097464 A166998 A038182
Adjacent sequences: A066236 A066237 A066238 * A066240 A066241 A066242
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Joseph L. Pe (joseph_l_pe(AT)hotmail.com), Dec 19 2001
|
| |
|
|
