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Template:Sequence of the Day for July 1

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Intended for: July 1, 2012

Timetable

  • First draft entered by Alonso del Arte on March 2, 2011 based on a write-up from October 24, 2010. ✓
  • Draft reviewed by Daniel Forgues on April 21, 2011
  • Draft approved by Harvey P. Dale June 17, 2011
  • Draft approved for re-use Dominion Day 2012 by Alonso del Arte on July 1, 2011
  • Slight emendation by Daniel Forgues on July 3, 2011
Yesterday's SOTD * Tomorrow's SOTD

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A070308: Numbers such that the sum of each base 10 digit squared adds up to the sum of the nontrivial divisors.

{ 125, 581, 8549, 16999 }

If we take the base 10 digits of these “Canada perfect numbers,” square each of them, and add them up, we find that they equal the sum of their nontrivial divisors (excluding 1 and the number itself). For example, with 125, we have 1 2 + 2 2 + 5 2 = 30. The divisors of 125 are 1, 5, 25, and 125, and we see that 5 and 25 ad up to 30. Prime numbers are excluded from consideration since their nontrivial divisors add up to 0.

These numbers were defined by mathematicians at the University of Manitoba to celebrate Canada’s 125 th anniversary.

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* Unfortunately, proper divisors commonly refer to aliquot divisors instead of nontrivial divisors in the mathematical literature.Daniel Forgues 21:33, 3 July 2011 (UTC)