A066239 The floor(1.001*x)-perfect numbers, where f-perfect numbers for an arithmetical function f are defined in A066218.

6, 28, 496, 32445, 130304, 388076, 199272950

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

Table of n, a(n) for n=1..7.

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

Cf. A066218.

Sequence in context: A060286 A000396 A152953 * A097464 A354072 A166998

Adjacent sequences: A066236 A066237 A066238 * A066240 A066241 A066242

Keyword

nonn,more

Author

Joseph L. Pe, Dec 19 2001

Extensions

a(5)-a(7) from Amiram Eldar, Sep 26 2019

Status

approved