1.3 KiB
id, title, challengeType, forumTopicId, dashedName
| id | title | challengeType | forumTopicId | dashedName |
|---|---|---|---|---|
| 5900f49b1000cf542c50ffad | Problem 302: Strong Achilles Numbers | 5 | 301956 | problem-302-strong-achilles-numbers |
--description--
A positive integer n is powerful if p^2 is a divisor of n for every prime factor p in n.
A positive integer n is a perfect power if n can be expressed as a power of another positive integer.
A positive integer n is an Achilles number if n is powerful but not a perfect power. For example, 864 and 1800 are Achilles numbers: 864 = 2^5 \times 3^3 and 1800 = 2^3 \times 3^2 \times 5^2.
We shall call a positive integer S a Strong Achilles number if both S and φ(S) are Achilles numbers. φ denotes Euler's totient function.
For example, 864 is a Strong Achilles number: φ(864) = 288 = 2^5 \times 3^2. However, 1800 isn't a Strong Achilles number because: φ(1800) = 480 = 2^5 \times 3^1 \times 5^1.
There are 7 Strong Achilles numbers below {10}^4 and 656 below {10}^8.
How many Strong Achilles numbers are there below {10}^{18}?
--hints--
strongAchillesNumbers() should return 1170060.
assert.strictEqual(strongAchillesNumbers(), 1170060);
--seed--
--seed-contents--
function strongAchillesNumbers() {
return true;
}
strongAchillesNumbers();
--solutions--
// solution required