1樓：畦哇矽
答案： 個。
解法：
對 進行素因數分解。
完全立方數的素因數分解中，每個素因數的指數都是 的倍數。而 的正因子中的完全立方數，素因子 的指數不大於 的對應指數。
也就是因子 的指數有 這 種選擇，因子 有 這 種選擇，因子 有 這 種選擇，因子 只有 這 種選擇。
總共的選擇數： 個。
完啦！不用往下翻了，下面沒東西。
解法二：
由已知，M=6658606584104736522240000000。
逐一檢驗[1,M]上的正整數，找出其中既能整除M，又是完全立方數的那些數。
檢驗發現共有468個正整數滿足條件，它們是：
1,8,27,64,125,216,343,512,729,1000,1728,2744,3375,4096,5832,8000,9261,13824,15625,19683,21952,27000,32768,42875,46656,64000,74088,91125,110592,125000,157464,175616,216000,250047,262144,343000,373248,421875,512000,531441,592704,729000,884736,1000000,1157625,1259712,1404928,1728000,2000376,2097152,2460375,2744000,2985984,3375000,4096000,4251528,4741632,5359375,5832000,6751269,7077888,8000000,9261000,10077696,11239424,11390625,13824000,14348907,16003008,16777216,19683000,21952000,23887872,27000000,31255875,32768000,34012224,37933056,42875000,46656000,54010152,56623104,64000000,66430125,74088000,80621568,89915392,91125000,110592000,114791256,128024064,134217728,144703125,157464000,175616000,182284263,191102976,216000000,250047000,262144000,272097792,303464448,307546875,343000000,373248000,432081216,452984832,512000000,531441000,592704000,644972544,719323136,729000000,843908625,884736000,918330048,1024192512,1073741824,1157625000,1259712000,1404928000,1458274104,1528823808,1728000000,1793613375,2000376000,2097152000,2176782336,2427715584,2460375000,2744000000,2985984000,3456649728,3623878656,3906984375,4096000000,4251528000,4741632000,4921675101,5159780352,5754585088,5832000000,6751269000,7077888000,7346640384,8193540096,8303765625,8589934592,9261000000,10077696000,11239424000,11666192832,12230590464,13824000000,14348907000,16003008000,16777216000,17414258688,19421724672,19683000000,21952000000,22785532875,23887872000,27653197824,28991029248,31255875000,32768000000,34012224000,37933056000,39373400808,41278242816,46036680704,46656000000,54010152000,56623104000,58773123072,65548320768,66430125000,68719476736,74088000000,80621568000,89915392000,93329542656,97844723712,105488578125,110592000000,114791256000,128024064000,134217728000,139314069504,155373797376,157464000000,175616000000,182284263000,191102976000,221225582592,224201671875,231928233984,250047000000,262144000000,272097792000,303464448000,314987206464,330225942528,368293445632,373248000000,432081216000,452984832000,470184984576,524386566144,531441000000,592704000000,615209387625,644972544000,719323136000,746636341248,782757789696,843908625000,884736000000,918330048000,1024192512000,1073741824000,1114512556032,1242990379008,1259712000000,1404928000000,1458274104000,1528823808000,1769804660736,1793613375000,1855425871872,2000376000000,2097152000000,2176782336000,2427715584000,2519897651712,2641807540224,2848191609375,2946347565056,2985984000000,3456649728000,3623878656000,3761479876608,4195092529152,4251528000000,4741632000000,4921675101000,5159780352000,5754585088000,5973090729984,6262062317568,6751269000000,7077888000000,7346640384000,8193540096000,8589934592000,8916100448256,9943923032064,10077696000000,11239424000000,11666192832000,12230590464000,14158437285888,14348907000000,16003008000000,16777216000000,17414258688000,19421724672000,20159181213696,21134460321792,22785532875000,23570780520448,23887872000000,27653197824000,28991029248000,30091839012864,33560740233216,34012224000000,37933056000000,39373400808000,41278242816000,46036680704000,47784725839872,50096498540544,54010152000000,56623104000000,58773123072000,65548320768000,71328803586048,76901173453125,79551384256512,80621568000000,89915392000000,93329542656000,97844723712000,113267498287104,114791256000000,128024064000000,134217728000000,139314069504000,155373797376000,161273449709568,169075682574336,182284263000000,191102976000000,221225582592000,231928233984000,240734712102912,268485921865728,272097792000000,303464448000000,314987206464000,330225942528000,368293445632000,382277806718976,432081216000000,452984832000000,470184984576000,524386566144000,570630428688384,615209387625000,636411074052096,644972544000000,719323136000000,746636341248000,782757789696000,906139986296832,918330048000000,1024192512000000,1073741824000000,1114512556032000,1242990379008000,1290187597676544,1352605460594688,1458274104000000,1528823808000000,1769804660736000,1925877696823296,2147887374925824,2176782336000000,2427715584000000,2519897651712000,2641807540224000,2946347565056000,3058222453751808,3456649728000000,3623878656000000,3761479876608000,4195092529152000,4565043429507072,4921675101000000,5159780352000000,5754585088000000,5973090729984000,6262062317568000,7249119890374656,7346640384000000,8193540096000000,8916100448256000,9943923032064000,10321500781412352,11666192832000000,12230590464000000,14158437285888000,15407021574586368,17183098999406592,17414258688000000,19421724672000000,20159181213696000,21134460321792000,24465779630014464,27653197824000000,28991029248000000,30091839012864000,33560740233216000,36520347436056576,39373400808000000,41278242816000000,46036680704000000,47784725839872000,57992959122997248,58773123072000000,65548320768000000,71328803586048000,79551384256512000,82572006251298816,93329542656000000,97844723712000000,113267498287104000,123256172596690944,139314069504000000,155373797376000000,161273449709568000,169075682574336000,195726237040115712,221225582592000000,240734712102912000,268485921865728000,314987206464000000,330225942528000000,368293445632000000,382277806718976000,463943672983977984,470184984576000000,524386566144000000,570630428688384000,660576050010390528,746636341248000000,782757789696000000,906139986296832000,986049380773527552,1114512556032000000,1242990379008000000,1290187597676544000,1565809896320925696,1769804660736000000,1925877696823296000,2147887374925824000,2519897651712000000,2641807540224000000,3058222453751808000,3761479876608000000,4195092529152000000,4565043429507072000,5284608400083124224,5973090729984000000,7249119890374656000,8916100448256000000,9943923032064000000,10321500781412352000,12526479170567405568,14158437285888000000,15407021574586368000,20159181213696000000,21134460321792000000,24465779630014464000,30091839012864000000,33560740233216000000,42276867200664993792,47784725839872000000,57992959122997248000,71328803586048000000,82572006251298816000,113267498287104000000,123256172596690944000,161273449709568000000,195726237040115712000,240734712102912000000,268485921865728000000,338214937605319950336,382277806718976000000,570630428688384000000,660576050010390528000,906139986296832000000,1290187597676544000000,1565809896320925696000,1925877696823296000000,3058222453751808000000,5284608400083124224000,7249119890374656000000,10321500781412352000000,15407021574586368000000,24465779630014464000000,42276867200664993792000,82572006251298816000000,195726237040115712000000,660576050010390528000000,5284608400083124224000000。完啦！
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