{"id":5173,"date":"2019-11-27T05:30:53","date_gmt":"2019-11-27T03:30:53","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=5173"},"modified":"2019-12-04T07:25:32","modified_gmt":"2019-12-04T05:25:32","slug":"menor-numero-triangular-con-mas-de-n-divisores","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/menor-numero-triangular-con-mas-de-n-divisores\/","title":{"rendered":"Menor n\u00famero triangular con m\u00e1s de n divisores"},"content":{"rendered":"<p>La sucesi\u00f3n de los <a href=\"http:\/\/bit.ly\/16xJtKZ\">n\u00fameros triangulares<\/a> se obtiene sumando los n\u00fameros naturales.<\/p>\n<pre lang=\"text\">\n   *     *      *        *         *   \n        * *    * *      * *       * *  \n              * * *    * * *     * * * \n                      * * * *   * * * *\n                               * * * * * \n   1     3      6        10        15\n<\/pre>\n<p>As\u00ed, el 7\u00ba n\u00famero triangular es<\/p>\n<pre lang=\"text\">\n   1 + 2 + 3 + 4 + 5 + 6 + 7 = 28. \n<\/pre>\n<p>Los primeros 10 n\u00fameros triangulares son<\/p>\n<pre lang=\"text\">\n   1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ...\n<\/pre>\n<p>Los divisores de los primeros 7 n\u00fameros triangulares son:<\/p>\n<pre lang=\"text\">\n    1: 1\n    3: 1,3\n    6: 1,2,3,6\n   10: 1,2,5,10\n   15: 1,3,5,15\n   21: 1,3,7,21\n   28: 1,2,4,7,14,28\n<\/pre>\n<p>Como se puede observar, 28 es el menor n\u00famero triangular con m\u00e1s de 5 divisores.<\/p>\n<p>Definir la funci\u00f3n<\/p>\n<pre lang=\"text\">\n   menorTriangularConAlMenosNDivisores :: Int -> Integer\n<\/pre>\n<p>tal que (menorTriangularConAlMenosNDivisores n) es el menor n\u00famero triangular que tiene al menos n divisores. Por ejemplo,<\/p>\n<pre lang=\"text\">\n   menorTriangularConAlMenosNDivisores 5    ==  28\n   menorTriangularConAlMenosNDivisores 50   ==  25200\n   menorTriangularConAlMenosNDivisores 500  ==  76576500\n<\/pre>\n<p><strong>Nota<\/strong>: Este ejercicio est\u00e1 basado en el <a href=\"https:\/\/projecteuler.net\/problem=12\">problema 12<\/a> del <a href=\"https:\/\/projecteuler.net\">Proyecto Euler<\/a><\/p>\n<h4>Soluciones<\/h4>\n<pre lang=\"haskell\">\nimport Data.List (group)\nimport Data.Numbers.Primes (primeFactors)\n\nmenorTriangularConAlMenosNDivisores :: Int -> Integer\nmenorTriangularConAlMenosNDivisores n = \n  head [x | x <- triangulares, nDivisores x >= n]\n\n-- Nota: Se usar\u00e1n las funciones\n-- + triangulares definida en [N\u00fameros triangulares](http:\/\/bit.ly\/2rtr6a3) y\n-- + nDivisores definida en [N\u00famero de divisores](http:\/\/bit.ly\/2DgVh74)\n\n-- triangulares es la sucesi\u00f3n de los n\u00fameros triangulares. Por ejemplo,\n--    take 10 triangulares  ==  [1,3,6,10,15,21,28,36,45,55]\ntriangulares :: [Integer]\ntriangulares = scanl1 (+) [1..]\n\n-- (nDivisores x) es el n\u00famero de divisores de x. Por ejemplo,\n--    nDivisores 28  ==  6\nnDivisores :: Integer -> Int\nnDivisores = product . map ((+1) . length) . group . primeFactors\n<\/pre>\n<h4>Pensamiento<\/h4>\n<blockquote><p>\n\u00abLa Matem\u00e1tica es una ciencia experimental y la computaci\u00f3n es el experimento.\u00bb ~ Rivin\n<\/p><\/blockquote>\n","protected":false},"excerpt":{"rendered":"<p>La sucesi\u00f3n de los n\u00fameros triangulares se obtiene sumando los n\u00fameros naturales. * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 1 3 6 10 15 As\u00ed, el 7\u00ba&#8230;<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_kad_post_transparent":"","_kad_post_title":"","_kad_post_layout":"","_kad_post_sidebar_id":"","_kad_post_content_style":"","_kad_post_vertical_padding":"","_kad_post_feature":"","_kad_post_feature_position":"","_kad_post_header":false,"_kad_post_footer":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"footnotes":"","_jetpack_memberships_contains_paid_content":false},"categories":[5],"tags":[8,481,13,71,28,10,11,247,157,252],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/5173"}],"collection":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/comments?post=5173"}],"version-history":[{"count":6,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/5173\/revisions"}],"predecessor-version":[{"id":5217,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/5173\/revisions\/5217"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=5173"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=5173"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=5173"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}