Aliquot sequence classifications: Difference between revisions
Added C++ solution
Thundergnat (talk | contribs) (Rename Perl 6 -> Raku, alphabetize, minor clean-up) |
(Added C++ solution) |
||
Line 571:
Integer : 153557177860800, Type : Non-Terminating, Series : 153557177860800, 470221741508000, 685337334283120, 908681172226160, 1276860840159280, 1867115442105104, 1751034184622896, 16436297
336056, 1405725265675144, 1230017019320456, 68719476751
</pre>
=={{header|C++}}==
This one follows the trail blazed by the "Number Theoretic" C example above.
<lang cpp>#include <cstdint>
#include <iostream>
#include <string>
using integer = uint64_t;
// See https://en.wikipedia.org/wiki/Divisor_function
integer divisor_sum(integer n) {
integer total = 1, power = 2;
// Deal with powers of 2 first
for (; n % 2 == 0; power *= 2, n /= 2)
total += power;
// Odd prime factors up to the square root
for (integer p = 3; p * p <= n; p += 2) {
integer sum = 1;
for (power = p; n % p == 0; power *= p, n /= p)
sum += power;
total *= sum;
}
// If n > 1 then it's prime
if (n > 1)
total *= n + 1;
return total;
}
// See https://en.wikipedia.org/wiki/Aliquot_sequence
void classify_aliquot_sequence(integer n) {
constexpr int limit = 16;
integer terms[limit];
terms[0] = n;
std::string classification("non-terminating");
int length = 1;
for (int i = 1; i < limit; ++i) {
++length;
terms[i] = divisor_sum(terms[i - 1]) - terms[i - 1];
if (terms[i] == n) {
classification =
(i == 1 ? "perfect" : (i == 2 ? "amicable" : "sociable"));
break;
}
int j = 1;
for (; j < i; ++j) {
if (terms[i] == terms[i - j])
break;
}
if (j < i) {
classification = (j == 1 ? "aspiring" : "cyclic");
break;
}
if (terms[i] == 0) {
classification = "terminating";
break;
}
}
std::cout << n << ": " << classification << ", sequence: " << terms[0];
for (int i = 1; i < length && terms[i] != terms[i - 1]; ++i)
std::cout << ' ' << terms[i];
std::cout << '\n';
}
int main() {
for (integer i = 1; i <= 10; ++i)
classify_aliquot_sequence(i);
for (integer i : {11, 12, 28, 496, 220, 1184, 12496, 1264460, 790, 909, 562,
1064, 1488})
classify_aliquot_sequence(i);
classify_aliquot_sequence(15355717786080);
classify_aliquot_sequence(153557177860800);
return 0;
}</lang>
{{out}}
<pre>
1: terminating, sequence: 1 0
2: terminating, sequence: 2 1 0
3: terminating, sequence: 3 1 0
4: terminating, sequence: 4 3 1 0
5: terminating, sequence: 5 1 0
6: perfect, sequence: 6
7: terminating, sequence: 7 1 0
8: terminating, sequence: 8 7 1 0
9: terminating, sequence: 9 4 3 1 0
10: terminating, sequence: 10 8 7 1 0
11: terminating, sequence: 11 1 0
12: terminating, sequence: 12 16 15 9 4 3 1 0
28: perfect, sequence: 28
496: perfect, sequence: 496
220: amicable, sequence: 220 284 220
1184: amicable, sequence: 1184 1210 1184
12496: sociable, sequence: 12496 14288 15472 14536 14264 12496
1264460: sociable, sequence: 1264460 1547860 1727636 1305184 1264460
790: aspiring, sequence: 790 650 652 496
909: aspiring, sequence: 909 417 143 25 6
562: cyclic, sequence: 562 284 220 284
1064: cyclic, sequence: 1064 1336 1184 1210 1184
1488: non-terminating, sequence: 1488 2480 3472 4464 8432 9424 10416 21328 22320 55056 95728 96720 236592 459792 881392 882384
15355717786080: non-terminating, sequence: 15355717786080 44534663601120 144940087464480 471714103310688 1130798979186912 2688948041357088 6050151708497568 13613157922639968 35513546724070632 74727605255142168 162658586225561832 353930992506879768 642678347124409032 1125102611548462968 1977286128289819992 3415126495450394808
153557177860800: non-terminating, sequence: 153557177860800 470221741508000 685337334283120 908681172226160 1276860840159280 1867115442105104 1751034184622896 1643629718341256 1441432897905784 1647351883321016 1557892692704584 1363939602434936 1194001297910344 1597170567336056 1405725265675144 1230017019320456
</pre>
| |||