Sequence: nth number with exactly n divisors: Difference between revisions
Sequence: nth number with exactly n divisors (view source)
Revision as of 02:42, 15 May 2021
, 3 years ago→{{header|Factor}}
Line 14:
:*[[Sequence: smallest number greater than previous term with exactly n divisors]]
:*[[Sequence: smallest number with exactly n divisors]]
=={{header|C++}}==
{{trans|Java}}
<lang cpp>#include <iostream>
#include <vector>
std::vector<int> smallPrimes;
bool is_prime(size_t test) {
if (test < 2) {
return false;
}
if (test % 2 == 0) {
return test == 2;
}
for (size_t d = 3; d * d <= test; d += 2) {
if (test % d == 0) {
return false;
}
}
return true;
}
void init_small_primes(size_t numPrimes) {
smallPrimes.push_back(2);
int count = 0;
for (size_t n = 3; count < numPrimes; n += 2) {
if (is_prime(n)) {
smallPrimes.push_back(n);
count++;
}
}
}
size_t divisor_count(size_t n) {
size_t count = 1;
while (n % 2 == 0) {
n /= 2;
count++;
}
for (size_t d = 3; d * d <= n; d += 2) {
size_t q = n / d;
size_t r = n % d;
size_t dc = 0;
while (r == 0) {
dc += count;
n = q;
q = n / d;
r = n % d;
}
count += dc;
}
if (n != 1) {
count *= 2;
}
return count;
}
uint64_t OEISA073916(size_t n) {
if (is_prime(n)) {
return (uint64_t) pow(smallPrimes[n - 1], n - 1);
}
size_t count = 0;
uint64_t result = 0;
for (size_t i = 1; count < n; i++) {
if (n % 2 == 1) {
// The solution for an odd (non-prime) term is always a square number
size_t root = (size_t) sqrt(i);
if (root * root != i) {
continue;
}
}
if (divisor_count(i) == n) {
count++;
result = i;
}
}
return result;
}
int main() {
const int MAX = 15;
init_small_primes(MAX);
for (size_t n = 1; n <= MAX; n++) {
if (n == 13) {
std::cout << "A073916(" << n << ") = One more bit needed to represent result.\n";
} else {
std::cout << "A073916(" << n << ") = " << OEISA073916(n) << '\n';
}
}
return 0;
}</lang>
{{out}}
<pre>A073916(1) = 1
A073916(2) = 3
A073916(3) = 25
A073916(4) = 14
A073916(5) = 14641
A073916(6) = 44
A073916(7) = 24137569
A073916(8) = 70
A073916(9) = 1089
A073916(10) = 405
A073916(11) = 819628286980801
A073916(12) = 160
A073916(13) = One more bit needed to represent result.
A073916(14) = 2752
A073916(15) = 9801</pre>
=={{header|Factor}}==
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