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

Author

Joseph L. Pe, Dec 19 2001

Keywords

• nonn
• more

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.

Examples

			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.
		

Links

• J. Pe, On a Generalization of Perfect Numbers, J. Rec. Math., 31(3) (2002-2003), 168-172.

Crossrefs

Cf. A066218.

Programs

Mathematica

f[x_] := Floor[1.001*x]; Select[ Range[1, 10^5], 2 * f[ # ] == Apply[ Plus, Map[ f, Divisors[ # ] ] ] & ]

Extensions

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