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Log Divisor Sum (Posted on 2014-08-01) Difficulty: 3 of 5
The sum of the base ten logarithms of the divisors of 10M is 792, where M is a positive integer.

What is the value of M?

No Solution Yet Submitted by K Sengupta    
Rating: 3.0000 (1 votes)

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Solution computer solution | Comment 1 of 2
DEFDBL A-Z
l2 = LOG(2) / LOG(10)
l5 = LOG(5) / LOG(10)

FOR m = 2 TO 20
    sum = 0
    FOR p2 = 0 TO m
        FOR p5 = 0 TO m
            sum = sum + p2 * l2 + p5 * l5
        NEXT
    NEXT
    PRINT m, sum
_clipboard$= _clipboard$+str$(m)+"   "+str$(sum)+chr$(13)+chr$(10)
NEXT

finds for different M:

 M    sum of logs of divisors
 2    9
 3    24
 4    50
 5    90
 6    147
 7    224
 8    323.9999999999998
 9    449.9999999999995
 10    604.9999999999992
 11    791.9999999999988
 12    1013.999999999998
 13    1273.999999999998
 14    1574.999999999998
 15    1919.999999999997
 16    2311.999999999997
 17    2753.999999999996
 18    3248.999999999996
 19    3799.999999999996
 20    4409.999999999995
 
 The larger amounts have rounding errors, but the sought value of M is 11.


  Posted by Charlie on 2014-08-01 12:36:02
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