median
don steward
mathematics teaching 10 ~ 16

Saturday, 21 December 2013

repeated factor sums

looking at the sum of the factors (apart from the number itself) leads to a study of abundant, deficient and perfect numbers

starting with the number 30

list all of the factors apart from the number itself and then sum these factors

do the same thing for this new number

and keep going:


30 ~ 1 + 2 + 3 + 5 + 6 + 10 + 15 = 42
42 ~ 1 + 2 + 3 + 6 + 7 + 14 + 21 = 54
54 ~ etc...

this gives an interesting sequence of numbers which increases in a steady pattern for a few terms (six altogether)

reasons for this aren't too difficult to consider (based on the number 6)

30 ~ 1, 2, 3, 6,     5, 10, 15
42 ~ 1, 2, 3, 6,     7, 14, 21
etc...

can similar 'runs' for other starting numbers be found?

what happens for 28?

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