{"id":586,"date":"2020-08-02T08:17:01","date_gmt":"2020-08-02T06:17:01","guid":{"rendered":"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/?p=586"},"modified":"2020-08-02T09:14:03","modified_gmt":"2020-08-02T07:14:03","slug":"numero-perfecto","status":"publish","type":"post","link":"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/numero-perfecto\/","title":{"rendered":"N\u00famero perfecto"},"content":{"rendered":"<p><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">Un n\u00famero es <strong>perfecto<\/strong> si la suma de todos sus divisores excepto \u00e9l coincide con dicho n\u00famero.<\/span><\/p>\n<p><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">Son n\u00fameros perfectos: 6, 28, 496, 8128, 33550336, 8589869056, 137438691328, &#8230;<\/span><\/p>\n<p><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">Div(6) = { 1 , 2 , 3 , 6 }&nbsp; \u2192&nbsp; 6 = 1 + 2 + 3<\/span><\/p>\n<p><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">Div(28) = { 1 , 2 , 4 , 7 , 14 , 28 }&nbsp; \u2192&nbsp; 28 = 1 + 2 + 4 + 7 + 14<\/span><\/p>\n<p><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">Div(496) = { 1 , 2 , 4 , 8 , 16 , 31 , 62 , 124 , 248 , 496 }&nbsp; \u2192&nbsp; 496 = 1+2+4+8+16+31+62+124+248<\/span><\/p>\n<p style=\"text-align: center\"><span style=\"font-family: 'times new roman', times, serif\">.&nbsp; &nbsp;.&nbsp; &nbsp;.&nbsp; &nbsp;.&nbsp; &nbsp;.&nbsp; &nbsp;.&nbsp; &nbsp;.<\/span><\/p>\n<p><span style=\"font-family: 'times new roman', times, serif\"><span style=\"font-size: 14pt\"><strong>Euclides<\/strong> descubri\u00f3 que si 2<\/span><span style=\"font-size: 14pt\"><sup>n<\/sup><span style=\"font-size: 14pt\">\u20131 es un n\u00famero primo, entonces 2<sup>n\u20131<\/sup><\/span><span style=\"font-size: 14pt\">\u00b7(2<sup>n<\/sup><\/span><span style=\"font-size: 14pt\">\u20131) es perfecto.<\/span><\/span><\/span><\/p>\n<p><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">n = 2&nbsp; (2<sup>2<\/sup>\u20131 = 3 primo)&nbsp; &nbsp;\u2192&nbsp; <span style=\"font-family: 'times new roman', times, serif\"><span style=\"font-size: 14pt\">2<sup>2\u20131<\/sup><\/span><\/span>\u00b7(2<sup>2<\/sup><span style=\"font-size: 14pt\">\u2013<\/span>1) = 2 \u00b7 3 = 6 perfecto.<\/span><\/p>\n<p><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">n = 3&nbsp; (2<sup>3<\/sup>\u20131 = 7 primo)&nbsp; &nbsp;\u2192&nbsp; <span style=\"font-size: 14pt\"><span style=\"font-family: 'times new roman', times, serif\">2<sup>3\u20131<\/sup><\/span><\/span>\u00b7(2<sup>3<\/sup><span style=\"font-size: 14pt\">\u20131<\/span>) = 4 \u00b7 7 = 28 perfecto<\/span><\/p>\n<p><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">n = 5&nbsp; (2<sup>5<\/sup>\u20131 = 31 primo)&nbsp; &nbsp;\u2192&nbsp; <span style=\"font-family: 'times new roman', times, serif\"><span style=\"font-size: 14pt\">2<sup>5\u20131<\/sup><\/span><\/span>\u00b7(2<sup>5<\/sup><span style=\"font-size: 14pt\">\u20131<\/span>) = 15 \u00b7 31 = 496 perfecto<\/span><\/p>\n<p><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">n = 7&nbsp; (2<sup>7<\/sup>\u20131 = 127 primo)&nbsp; &nbsp;\u2192&nbsp; <span style=\"font-family: 'times new roman', times, serif\"><span style=\"font-size: 14pt\">2<sup>7\u20131<\/sup><\/span><\/span>\u00b7(2<sup>7<\/sup><span style=\"font-size: 14pt\">\u20131<\/span>) = 64 \u00b7 127 =&nbsp; 8128 perfecto<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Un n\u00famero es perfecto si la suma de todos sus divisores excepto \u00e9l coincide con dicho n\u00famero. Son n\u00fameros perfectos: 6, 28, 496, 8128, 33550336, 8589869056, 137438691328, &#8230; Div(6) = { 1 , 2&#46;&#46;&#46;<\/p>\n","protected":false},"author":7927,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"ngg_post_thumbnail":0,"footnotes":""},"categories":[2075204],"tags":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/wp-json\/wp\/v2\/posts\/586"}],"collection":[{"href":"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/wp-json\/wp\/v2\/users\/7927"}],"replies":[{"embeddable":true,"href":"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/wp-json\/wp\/v2\/comments?post=586"}],"version-history":[{"count":7,"href":"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/wp-json\/wp\/v2\/posts\/586\/revisions"}],"predecessor-version":[{"id":593,"href":"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/wp-json\/wp\/v2\/posts\/586\/revisions\/593"}],"wp:attachment":[{"href":"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/wp-json\/wp\/v2\/media?parent=586"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/wp-json\/wp\/v2\/categories?post=586"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/wp-json\/wp\/v2\/tags?post=586"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}