Pseudoperfect Number

Author

Eric W. Weisstein
December 7, 2013

This notebook downloaded from http://mathworld.wolfram.com/notebooks/NumberTheoreticFunctions/PseudoperfectNumber.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/PseudoperfectNumber.html.

©2013 Wolfram Research, Inc. except for portions noted otherwise

Enumeration

(l1=Select[Range[100], PseudoperfectQ])// Timing

(l2=Select[Range[100],PseudoperfectQ[#,Method->"Knapsack"]&])//Timing

Complement[l1,l2]

Divisors/@%

Special cases

FindInstance[a+b==a b&&a>0&&b>0&&a≠b,{a,b},Integers]

FindInstance[a+b+c==a b c&&a>0&&b>0&&c>0,{a,b,c},Integers]

FindInstance[1+b+c==b c&&b>0&&c>0,{b,c},Integers]

FindInstance[1+b+c+d==b c d&&b>0&&c>0&&d>0&&1≠b≠c≠d,{b,c,d},Integers]//Timing

FindInstance[a+b+c+d==a b c d&&a>0&&b>0&&c>0&&d>0&&a≠b≠c≠d,{a,b,c,d},Integers]//Timing

FindInstance[1+b+c+d+e==b c d e&&b>0&&c>0&&d>0&&e>0&&1≠b≠c≠d≠e,{b,c,d,e},Integers]//Timing