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 Summing the factors (Posted on 2018-03-08)
Let N=24* 57.

What is the sum of all N's positive factors?

Generalize.

 See The Solution Submitted by Ady TZIDON No Rating

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 re: a solution Comment 2 of 2 |
(In reply to a solution by Charlie)

Without using directly the sigma function, it is possible to relay on the sum of geometric sequences. When the first term is 1 the terms of the sequence are the successive potences of the ratio.

1+a+a^2+ ... +a^n = [a^(n+1)-1]/(a-1)

For (a, b)=(2, 5)

S= (2^(m+1)-1)*(5^(n+1)-1)/4

For (m,n) = (4,7)
S= (2^5-1)*(5^8-1)/4 = 31*390624/4 = 3027336

For general number (a,b) and potences (m,n)

S=[(a^(m+1)-1)*(b^(n+1)-1]/[(a-1)*(b-1)]

which is true only if there is no pair (i, j) that a^m*b^n = a^i*b^j

Edited on March 9, 2018, 5:48 am
 Posted by armando on 2018-03-09 03:42:06

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