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A126029
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The smallest positive k such that ( sopfr(k)*tau(k) )^n = sigma(k) where sopfr is the sum of prime factors with multiplicity (A001414).
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1
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OFFSET
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1,1
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COMMENTS
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35 is the only solution for n=1.
Incorrect, there are three solutions < 10^10 for n = 1: 35, 42 and 68. - Donovan Johnson, Jun 11 2013
a(3) = 14844221560107739 (conjectured) is most likely minimal but it hasn't been proved. No solutions have been found (minimal or otherwise) where the number was not squarefree.
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LINKS
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FORMULA
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EXAMPLE
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22446139 factors as: 31*67*101*107=k, sopfr(k) = sum of prime factors of k = 31+67+101+107 = 306. tau(k) = num of divisors of k = 2^4 = 16. sigma(k) = sum of divisors of k = (31+1)*(67+1)*(101+1)*(107+1) = 23970816. (306*16)^2 = 23970816. As this k turns out to be minimal, a(2)=22446139.
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CROSSREFS
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KEYWORD
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hard,nonn,bref
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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