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Code Golf

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Calculate the lowest number where the sum of the sequence of numbers exceeds a given value

Given you have an infinite sequence of numbers defined as follows:

1: 1 = 1
2: 1 + 2 = 3
3: 1 + 3 = 4
4: 1 + 2 + 4 = 7
5: 1 + 5 = 6
6: 1 +たす 2 +たす 3 +たす 6 =わ 12
7: 1 + 7 = 8
...

The sequence is the sum of the divisors of n, including 1 and n.

Given a positive integer x as input, calculate the lowest number n which will produce a result greater than x.

Test cases

f(100) = 48, ∑ = 124
f(25000) = 7200, ∑ = 25389
f(5000000) = 1164240, ∑ = 5088960

Expected Output

Your program should return both n and the sum of its divisors, like so:

$ ./challenge 100
48,124

Rules

This is code-golf so the shortest code in bytes, in each language wins.

Answer*

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  • \$\begingroup\$ 77 bytes. \$\endgroup\$ Commented Dec 4, 2017 at 16:14
  • \$\begingroup\$ Replacing the tabs with two spaces makes this work in python 3 at 83 bytes, although to try it I had to put parentheses in the print statement. You can also replace the return statement with a print statement and not need an auxiliary function to print it; the bytes stay the same. \$\endgroup\$ Commented Jul 15, 2018 at 7:05

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