%I #17 Jan 30 2026 13:36:30

%S 5,7,11,49,169

%N The floor(prime(n)/n)-perfect numbers, where prime(n) denotes the n-th prime and f-perfect numbers for an arithmetical function f are defined in A066218.

%C There do not seem to be any more terms. There are no terms between 170 and 10^5.

%H Joseph L. Pe, <a href="https://vixra.org/abs/2503.0165">On a Generalization of Perfect Numbers</a>, J. Rec. Math., 31(3) (2002-2003), 168-172.

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

%Y Cf. A038605, A066218.

%K nonn,more

%O 1,1

%A _Joseph L. Pe_, Dec 21 2001