85 lines
5.4 KiB
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85 lines
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<h2>Harshad Numbers</h2><div class="info" style="cursor:help;width:200px;margin-bottom:10px;"><h3>Problem 387</h3><span style="width:300px;color:#666;">Published on Sunday, 3rd June 2012, 11:00 am; Solved by 892</span></div>
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<P>A <b>Harshad or Niven number</b> is a number that is divisible by the sum of its digits.
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<BR/>201 is a Harshad number because it is divisible by 3 (the sum of its digits.)
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<BR/>When we truncate the last digit from 201, we get 20, which is a Harshad number.
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<BR/>When we truncate the last digit from 20, we get 2, which is also a Harshad number.
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<BR/>Let's call a Harshad number that, while recursively truncating the last digit, always results in a Harshad number a <i>right truncatable Harshad number.</i></P>
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<P>Also:
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<BR/>201/3=67 which is prime.
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<BR/>Let's call a Harshad number that, when divided by the sum of its digits, results in a prime a <i>strong Harshad number</i>.</P>
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<P>Now take the number 2011 which is prime.
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<BR/>When we truncate the last digit from it we get 201, a strong Harshad number that is also right truncatable.
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<BR/>Let's call such primes <i>strong, right truncatable Harshad primes</i>.</P>
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<P>You are given that the sum of the strong, right truncatable Harshad primes less than 10000 is 90619.</P>
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<P>Find the sum of the strong, right truncatable Harshad primes less than 10<sup>14</sup>.</P>
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