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Triangular Transcension (Posted on 2009-09-22) Difficulty: 3 of 5
Determine the minimum value of a triangular number T such that the total number of positive divisors of T, including 1 and T, exceeds 500.

See The Solution Submitted by K Sengupta    
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Solution UBASIC version Comment 3 of 3 |
list
   10   Tr=1:Trn=1
   20   loop
   30       Tr=Tr+1:Trn=Trn+Tr
   40       Dvsrs=fnDivs(Trn)
   50       if Dvsrs>=500 then print Tr;Trn;Dvsrs:end
   60   endloop
  499   end
  500   fnDivs(X)
  510   local Ds,Ct,Pdr
  550   Ds=1:Ct=0:Pdr=0
  570   N=X
  580   while N>1
  590      Dr=prmdiv(N)
  600      N=N//Dr
  610      if Dr=Pdr then Ct=Ct+1
  620        :else Ds=Ds*(Ct+1)
  630           :Ct=1
  640      Pdr=Dr
  650   wend
  660   Ds=Ds*(Ct+1)
  670   return(Ds)
OK
run
 12375  76576500  576
OK

  Posted by Charlie on 2009-09-23 00:52:01
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