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Rev

Required fields*

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*

# [Python 3], 100 bytes



 d=lambda y:sum(i+1for i in range(y)if y%-~i<1)
 f=lambda x:min((j,d(j))for j in range(x+1)if x<=d(j))

[Try it online!][TIO-jaraogs9]

[Python 3]: https://docs.python.org/3/
[TIO-jaraogs9]: https://tio.run/##K6gsycjPM/7/P8U2JzE3KSVRodKquDRXI1PbMC2/SCFTITNPoSgxLz1Vo1IzM02hUlW3LtPGUJMrDaa8wio3M09DI0snRSNLUxOkJwuhp0LbEKSrwsYWLPu/oCgzr0QjTcNQU5MLzjYwAPKUYVwjUwOQwH8A "Python 3 – Try It Online"

Thanks to [Jonathan Frech](https://codegolf.stackexchange.com/users/73111/jonathan-frech)'s comment on the previous python 3 attempt, I have just greatly expanded my knowledge of python syntax. I'd never have thought of the -~i for i+1 trick, which saves two characters.

However, that answer is 1) not minimal and 2) doesn't work for x=1 (due to an off-by-one error which is easy to make while going for brevity; I suggest everyone else check their answers for this edge case!).

Quick explanation:
`sum(i+1for i in range(y)if y%-~i<1)` is equivalent to `sum(i for i in range(1,y+1)if y%i<1)` but saves two characters. Thanks again to Mr. Frech.

`d=lambda y:sum(i+1for i in range(y)if y%-~i<1)` therefore returns the divisors of y.

`f=lambda x:min((j,d(j))for j in range(x+1)if x<=d(j))` is where I really did work. Since comparing a tuple works in dictionary order, we can compare j,d(j) as easily as we can compare j, and this lets us not have to find the minimal j, store it in a variable, and /then/ compute the tuple in a separate operation. Also, we have to have the <=, not <, in `x<=d(j)`, because d(1) is 1 so if x is 1 you get nothing. This is also why we need `range(x+1)` and not `range(x)`.

I'd previously had d return the tuple, but then I have to subscript it in f, so that takes three more characters.

If this is an answer to a challenge…

…Be sure to follow the challenge specification. However, please refrain from exploiting obvious loopholes. Answers abusing any of the standard loopholes are considered invalid. If you think a specification is unclear or underspecified, comment on the question instead.
…Try to optimize your score. For instance, answers to code-golf challenges should attempt to be as short as possible. You can always include a readable version of the code in addition to the competitive one. Explanations of your answer make it more interesting to read and are very much encouraged.
…Include a short header which indicates the language(s) of your code and its score, as defined by the challenge.

More generally…

…Please make sure to answer the question and provide sufficient detail.
…Avoid asking for help, clarification or responding to other answers (use comments instead).

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\$\begingroup\$ Welcome to the site and nice first post. You can get to 98 bytes by removing the f= as anonymous functions are perfectly acceptable here! \$\endgroup\$

caird coinheringaahing
– caird coinheringaahing ♦

2017年12月03日 21:59:01 +00:00
Commented Dec 3, 2017 at 21:59
\$\begingroup\$ You can't call an anonymous function from another line of code, is the problem -- I have a separate print(f(100)) statement to test that the function works. \$\endgroup\$

Sam Howard
– Sam Howard

2017年12月03日 22:02:54 +00:00
Commented Dec 3, 2017 at 22:02
\$\begingroup\$ That's not a problem here. It's perfectly acceptable and works to not include the f= in your byte count, and is a good way to golf in Python. Check this for more golfing tips in Python! \$\endgroup\$

caird coinheringaahing
– caird coinheringaahing ♦

2017年12月03日 22:05:22 +00:00
Commented Dec 3, 2017 at 22:05
\$\begingroup\$ Hm. I can equal, but not better, my submission by appending q=range and replacing range with q in both existing instances. Sadly, this doesn't improve it and since lambda is a keyword I can't use it for that, I'd have to do exec() tricks wasting too many characters. \$\endgroup\$

Sam Howard
– Sam Howard

2017年12月04日 15:32:52 +00:00
Commented Dec 4, 2017 at 15:32
\$\begingroup\$ @MichaelBoger Well, you can call an anonymous function in Python; lambda expressions do not have to be assigned to a variable. \$\endgroup\$

Jonathan Frech
– Jonathan Frech

2017年12月04日 16:10:40 +00:00
Commented Dec 4, 2017 at 16:10

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