primary pseudoperfect number

Given an integer n with ω(n) distinct prime factors pi (where ω is number of distinct prime factors function), if the equality


holds true, then n is a primary pseudoperfect number. Equivalently,


if n is a primary pseudoperfect number.

The first few primary pseudoperfect numbers are 2, 6, 42, 1806, 47058, 2214502422, 52495396602, 8490421583559688410706771261086, the first four of these being each one less than the first four terms of Sylvester’s sequence; these are listed in A054377 of Sloane’s OEIS. Presently it’s not known whether there are any odd primary pseudoperfect numbers.

Title primary pseudoperfect number
Canonical name PrimaryPseudoperfectNumber
Date of creation 2013-03-22 16:17:40
Last modified on 2013-03-22 16:17:40
Owner CompositeFan (12809)
Last modified by CompositeFan (12809)
Numerical id 6
Author CompositeFan (12809)
Entry type Definition
Classification msc 11D85
Related topic GiugaNumber