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## to Perfect Numbers in the Erlang Track

Published at Feb 09 2021 · 0 comments
Instructions
Test suite
Solution

Determine if a number is perfect, abundant, or deficient based on Nicomachus' (60 - 120 CE) classification scheme for natural numbers.

The Greek mathematician Nicomachus devised a classification scheme for natural numbers, identifying each as belonging uniquely to the categories of perfect, abundant, or deficient based on their aliquot sum. The aliquot sum is defined as the sum of the factors of a number not including the number itself. For example, the aliquot sum of 15 is (1 + 3 + 5) = 9

• Perfect: aliquot sum = number
• 6 is a perfect number because (1 + 2 + 3) = 6
• 28 is a perfect number because (1 + 2 + 4 + 7 + 14) = 28
• Abundant: aliquot sum > number
• 12 is an abundant number because (1 + 2 + 3 + 4 + 6) = 16
• 24 is an abundant number because (1 + 2 + 3 + 4 + 6 + 8 + 12) = 36
• Deficient: aliquot sum < number
• 8 is a deficient number because (1 + 2 + 4) = 7
• Prime numbers are deficient

Implement a way to determine whether a given number is perfect. Depending on your language track, you may also need to implement a way to determine whether a given number is abundant or deficient.

## Running tests

In order to run the tests, issue the following command from the exercise directory:

For running the tests provided, `rebar3` is used as it is the official build and dependency management tool for erlang now. Please refer to the tracks installation instructions on how to do that.

In order to run the tests, you can issue the following command from the exercise directory.

``````\$ rebar3 eunit
``````

## Questions?

For detailed information about the Erlang track, please refer to the help page on the Exercism site. This covers the basic information on setting up the development environment expected by the exercises.

## Source

Taken from Chapter 2 of Functional Thinking by Neal Ford. http://shop.oreilly.com/product/0636920029687.do

## Submitting Incomplete Solutions

It's possible to submit an incomplete solution so you can see how others have completed the exercise.

### perfect_numbers_tests.erl

``````%% Generated with 'testgen v0.2.0'
%% Revision 1 of the exercises generator was used
%% https://github.com/exercism/problem-specifications/raw/fcbc25191f449f3791db0f2e8acf2d670ea138a0/exercises/perfect-numbers/canonical-data.json
%% This file is automatically generated from the exercises canonical data.

-module(perfect_numbers_tests).

-include_lib("erl_exercism/include/exercism.hrl").
-include_lib("eunit/include/eunit.hrl").

'1_smallest_perfect_number_is_classified_correctly_test_'() ->
{"Smallest perfect number is classified "
"correctly",
?_assertEqual(perfect, perfect_numbers:classify(6))}.

'2_medium_perfect_number_is_classified_correctly_test_'() ->
{"Medium perfect number is classified "
"correctly",
?_assertEqual(perfect, perfect_numbers:classify(28))}.

'3_large_perfect_number_is_classified_correctly_test_'() ->
{"Large perfect number is classified correctly",
?_assertEqual(perfect,
perfect_numbers:classify(33550336))}.

'4_smallest_abundant_number_is_classified_correctly_test_'() ->
{"Smallest abundant number is classified "
"correctly",
?_assertEqual(abundant, perfect_numbers:classify(12))}.

'5_medium_abundant_number_is_classified_correctly_test_'() ->
{"Medium abundant number is classified "
"correctly",
?_assertEqual(abundant, perfect_numbers:classify(30))}.

'6_large_abundant_number_is_classified_correctly_test_'() ->
{"Large abundant number is classified "
"correctly",
?_assertEqual(abundant,
perfect_numbers:classify(33550335))}.

'7_smallest_prime_deficient_number_is_classified_correctly_test_'() ->
{"Smallest prime deficient number is classified "
"correctly",
?_assertEqual(deficient, perfect_numbers:classify(2))}.

'8_smallest_non_prime_deficient_number_is_classified_correctly_test_'() ->
{"Smallest non-prime deficient number "
"is classified correctly",
?_assertEqual(deficient, perfect_numbers:classify(4))}.

'9_medium_deficient_number_is_classified_correctly_test_'() ->
{"Medium deficient number is classified "
"correctly",
?_assertEqual(deficient, perfect_numbers:classify(32))}.

'10_large_deficient_number_is_classified_correctly_test_'() ->
{"Large deficient number is classified "
"correctly",
?_assertEqual(deficient,
perfect_numbers:classify(33550337))}.

'11_edge_case_no_factors_other_than_itself_is_classified_correctly_test_'() ->
{"Edge case (no factors other than itself) "
"is classified correctly",
?_assertEqual(deficient, perfect_numbers:classify(1))}.

'12_zero_is_rejected_as_it_is_not_a_positive_integer_test_'() ->
{"Zero is rejected (as it is not a positive "
"integer)",
?_assertError(_, perfect_numbers:classify(0))}.

'13_negative_integer_is_rejected_as_it_is_not_a_positive_integer_test_'() ->
{"Negative integer is rejected (as it "
"is not a positive integer)",
?_assertError(_, perfect_numbers:classify(-1))}.``````
``````-module(perfect_numbers).

-export([classify/1]).

aliquot(Num) ->
case Num of
X when X < 1 -> erlang:error(badarg);
1 -> 0;
_ ->
MaxIndex = trunc(math:sqrt(Num)),
aliquot(Num, MaxIndex, 2, 1)
end.

aliquot(_Num, ISqrt, Index, Acc) when Index > ISqrt -> Acc;
aliquot(Num, ISqrt, Index, Acc) ->
case Num rem Index of
0 ->
LargerDiv = Num div Index,
NewAcc = Acc + Index + (case LargerDiv of X when X > Index -> X; _ -> 0 end),
aliquot(Num, ISqrt, Index + 1, NewAcc);
_ -> aliquot(Num, ISqrt, Index + 1, Acc)
end.

classify(Num) ->
case aliquot(Num) - Num of
0 -> perfect;
Positive when Positive > 0 -> abundant;
_ -> deficient
end.``````

## Community comments

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### What can you learn from this solution?

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