Need help finding a value of Sigma(n) or σ(n)?
I need to find the smallest value of k, so that
σ(1) + σ(2) + ... + σ(k) ≠ σ(n) for any integer n.
I went through and found that σ(n) ≠ 2, 5, 9, 11, 16...
And was trying to find a left side that equaled one of these values. But I'm not sure how many I'll have to test, and was wondering if there was an easier way to solve this.
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I'm not sure whether or not there's a simple way to solve this, but the smallest value of k is 5.
σ(1) = 1 = σ(1)
σ(1) + σ(2) = 1 + 3 = 4 = σ(3)
σ(1) + ... + σ(3) = 4 + 4 = 8 = σ(7)
σ(1) + ... + σ(4) = 8 + 7 = 15 = σ(8)
σ(1) + ... + σ(5) = 15 + 6 = 21
Checking σ(n) for n ≤ 21, we find σ(n) ≠ 21.
So k = 5.