A066238 The floor(n/3)-perfect numbers, where f-perfect numbers for an arithmetical function f are defined in A066218.

2, 12, 18, 40, 56, 304, 550, 748, 1504, 3230, 3770, 6976, 29824, 124672, 351351, 382772, 510464, 537248, 698528, 791264, 1081568, 1279136, 2065408, 2279072, 211855016, 561841408, 731378944, 3365232128, 3557004544

Offset

1,1

Comments

It appears that there are more floor(n/N)-perfect numbers the larger N is. (Here N = 3.)

Links

Table of n, a(n) for n=1..29.

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

Example

Let f(n) = floor(n/3). Then f(12) = 6 = 3+2+1+0 = f(6)+f(4)+f(3)+f(1); so 12 is a term of the sequence.

Mathematica

f[x_] := Floor[x/3]; Select[ Range[2, 10^5], 2 * f[ # ] == Apply[ Plus, Map[ f, Divisors[ # ] ] ] & ]

Crossrefs

Cf. A066218.

Sequence in context: A325767 A335799 A190044 * A101074 A115109 A048001

Adjacent sequences: A066235 A066236 A066237 * A066239 A066240 A066241

Keyword

nonn,more

Author

Joseph L. Pe, Dec 19 2001

Extensions

a(14)-a(29) from Amiram Eldar, Sep 26 2019

Status

approved