Question 201989: What is the smallest composite number over 10,000 whose digits sum to the same value as the sum of the digits of its prime factorization?
Found 2 solutions by Alan3354, RAY100:
Answer by Alan3354(69443)   (Show Source):
Answer by RAY100(1637)  (Show Source):
You can put this solution on YOUR website! Try this, assume that the digits are the same,
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xx,xxx,,,,,or x+x+x+x+x (Sum of Digits)
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if y = factor,,,,use 5 factors(somewhat arbitrary),again all factors same
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As a 1st est,,,5th root of 10000 = 6.3,, therefore use 7
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7^5 = 16,807,,,1+6+8+0+7 = 22 vs 5*7 =35
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trying 8, 8^5 = 32768,,,,3+2+7+6+8=26, vs 5*8=40
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from this pattern we see that the power should increase, and the base degrease
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following this pattern, bring us to 3^9= 19683
Sum of Digits = 1+9+6+8+3 = 27,,,and 9*3 =27
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Might be a number closer to 10,000, but this works
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