62 lines
1.7 KiB
JavaScript
62 lines
1.7 KiB
JavaScript
(function (max) {
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// Proper divisors
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function properDivisors(n) {
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if (n < 2) return [];
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else {
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var rRoot = Math.sqrt(n),
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intRoot = Math.floor(rRoot),
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lows = range(1, intRoot).filter(function (x) {
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return (n % x) === 0;
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});
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return lows.concat(lows.slice(1).map(function (x) {
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return n / x;
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}).reverse().slice((rRoot === intRoot) | 0));
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}
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}
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// [m..n]
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function range(m, n) {
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var a = Array(n - m + 1),
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i = n + 1;
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while (i--) a[i - 1] = i;
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return a;
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}
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// Filter an array of proper divisor sums,
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// reading the array index as a function of N (N-1)
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// and the sum of proper divisors as a potential M
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var pairs = range(1, max).map(function (x) {
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return properDivisors(x).reduce(function (a, d) {
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return a + d;
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}, 0)
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}).reduce(function (a, m, i, lst) {
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var n = i + 1;
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return (m > n) && lst[m - 1] === n ? a.concat([[n, m]]) : a;
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}, []);
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// [[a]] -> bool -> s -> s
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function wikiTable(lstRows, blnHeaderRow, strStyle) {
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return '{| class="wikitable" ' + (
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strStyle ? 'style="' + strStyle + '"' : ''
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) + lstRows.map(function (lstRow, iRow) {
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var strDelim = ((blnHeaderRow && !iRow) ? '!' : '|');
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return '\n|-\n' + strDelim + ' ' + lstRow.map(function (v) {
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return typeof v === 'undefined' ? ' ' : v;
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}).join(' ' + strDelim + strDelim + ' ');
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}).join('') + '\n|}';
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}
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return wikiTable(
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[['N', 'M']].concat(pairs),
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true,
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'text-align:center'
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) + '\n\n' + JSON.stringify(pairs);
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})(20000);
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