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 Log Divisor Sum (Posted on 2014-08-01)
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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 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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