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| 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 p2 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 = 25·33 and 1800 = 23·32·52.
We shall call a positive integer S a Strong Achilles number if both S and φ(S) are Achilles numbers.1 For example, 864 is a Strong Achilles number: φ(864) = 288 = 25·32. However, 1800 isn't a Strong Achilles number because: φ(1800) = 480 = 25·31·51.
There are 7 Strong Achilles numbers below 104 and 656 below 108.
How many Strong Achilles numbers are there below 1018?
1 φ denotes Euler's totient function.
--hints--
euler302() should return 1170060.
assert.strictEqual(euler302(), 1170060);
--seed--
--seed-contents--
function euler302() {
return true;
}
euler302();
--solutions--
// solution required