For which of the following expressions is there no value of n>1 for which the given sum is a square?:

1+2+3+...+n
1+3+5+...+(2*n-1)
1+4+7+...+(3*n-2)
1+5+9+...+(4*n-3)
1+6+11+...+(5*n-4)
1+7+13+...+(6*n-5)
1+8+15+...+(7*n-6)
1+9+17+...+(8*n-7)

Also:

For which two of them are there values of n such that the sum is the perfect number 2,305,843,008,139,952,128?

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From BENT Brain Ticklers, Winter 2024

f(k,n) = (kn^2 - kn + 2n) / 2

Posted by Larry on 2025-02-23 10:29:18