Problems & Puzzles: Puzzles

Puzzle 939. Numbers in Arithmetical progression whose sum of divisors is same (CYF 35) Fred Schneider sent the following nice puzzle: 1: 1 = sigma(1)  => Trivial 2: 12 = sigma(6) = sigma(11) => Common difference: 5 3: 360 = sigma(267) = sigma(295) = sigma(323) => Common difference: 28 4: 119508480 = sigma(34560288) = sigma(36699180) = sigma(38838072) = sigma(40976964) => Common Difference: 2138892 5: 1666818611640000 =  sigma(1666818506570911) =  sigma(1666818512348641) = sigma(1666818518126371) =  sigma(1666818523904101) =  sigma(1666818529681831) => Common Difference: 5777730 From CYU #35 at http://www.shyamsundergupta.com/canyoufind.htm:  The answer for 4 is the smallest known solution.   The answer for 5 is the only known solution. J. Wroblewski found this using a parametric equation(!) Q1. Confirm this is the smallest answer for 4 Q2. Find a smaller solution to 5  Q3. Extend the list

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Contribution came from Fred Schneider

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Fred wrote on Jan 20, 2109:

Using brute force, I found the minimal answer to  #1

The numbers: 37558049, 38590133, 39622217, 40654301
have a difference of 1032084 and have common sigma = 41057280

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