Ruth-Aaron numbers: Difference between revisions
Added C++ solution
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(Added C++ solution) |
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;*[[oeis:A006145|OEIS:A006145 - Ruth-Aaron numbers (1): sum of prime divisors of n = sum of prime divisors of n+1]]
;*[[oeis:A039752|OEIS:A039752 - Ruth-Aaron numbers (2): sum of prime divisors of n = sum of prime divisors of n+1 (both taken with multiplicity)]]
=={{header|C++}}==
This takes about 2 minutes 24 seconds (3.2GHz Quad-Core Intel Core i5).
<lang cpp>#include <iomanip>
#include <iostream>
int prime_factor_sum(int n) {
int sum = 0;
for (; (n & 1) == 0; n >>= 1)
sum += 2;
for (int p = 3, sq = 9; sq <= n; p += 2) {
for (; n % p == 0; n /= p)
sum += p;
sq += (p + 1) << 2;
}
if (n > 1)
sum += n;
return sum;
}
int prime_divisor_sum(int n) {
int sum = 0;
if ((n & 1) == 0) {
sum += 2;
n >>= 1;
while ((n & 1) == 0)
n >>= 1;
}
for (int p = 3, sq = 9; sq <= n; p += 2) {
if (n % p == 0) {
sum += p;
n /= p;
while (n % p == 0)
n /= p;
}
sq += (p + 1) << 2;
}
if (n > 1)
sum += n;
return sum;
}
int main() {
const int limit = 30;
int dsum1 = 0, fsum1 = 0, dsum2 = 0, fsum2 = 0;
std::cout << "First " << limit << " Ruth-Aaron numbers (factors):\n";
for (int n = 2, count = 0; count < limit; ++n) {
fsum2 = prime_factor_sum(n);
if (fsum1 == fsum2) {
++count;
std::cout << std::setw(5) << n - 1
<< (count % 10 == 0 ? '\n' : ' ');
}
fsum1 = fsum2;
}
std::cout << "\nFirst " << limit << " Ruth-Aaron numbers (divisors):\n";
for (int n = 2, count = 0; count < limit; ++n) {
dsum2 = prime_divisor_sum(n);
if (dsum1 == dsum2) {
++count;
std::cout << std::setw(5) << n - 1
<< (count % 10 == 0 ? '\n' : ' ');
}
dsum1 = dsum2;
}
dsum1 = 0, fsum1 = 0, dsum2 = 0, fsum2 = 0;
for (int n = 2;; ++n) {
int fsum3 = prime_factor_sum(n);
if (fsum1 == fsum2 && fsum2 == fsum3) {
std::cout << "\nFirst Ruth-Aaron triple (factors): " << n - 2
<< '\n';
break;
}
fsum1 = fsum2;
fsum2 = fsum3;
}
for (int n = 2;; ++n) {
int dsum3 = prime_divisor_sum(n);
if (dsum1 == dsum2 && dsum2 == dsum3) {
std::cout << "\nFirst Ruth-Aaron triple (divisors): " << n - 2
<< '\n';
break;
}
dsum1 = dsum2;
dsum2 = dsum3;
}
}</lang>
{{out}}
<pre>
First 30 Ruth-Aaron numbers (factors):
5 8 15 77 125 714 948 1330 1520 1862
2491 3248 4185 4191 5405 5560 5959 6867 8280 8463
10647 12351 14587 16932 17080 18490 20450 24895 26642 26649
First 30 Ruth-Aaron numbers (divisors):
5 24 49 77 104 153 369 492 714 1682
2107 2299 2600 2783 5405 6556 6811 8855 9800 12726
13775 18655 21183 24024 24432 24880 25839 26642 35456 40081
First Ruth-Aaron triple (factors): 417162
First Ruth-Aaron triple (divisors): 89460294
</pre>
=={{header|J}}==
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