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A247653
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Write 2n as a product of numbers of the form 4k+2 (A016825) so as to minimize the sum of the factors; a(n) is this sum.
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2
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2, 4, 6, 6, 10, 8, 14, 8, 18, 12, 22, 10, 26, 16, 30, 10, 34, 12, 38, 14, 42, 24, 46, 12, 50, 28, 54, 18, 58, 16, 62, 12, 66, 36, 70, 14, 74, 40, 78, 16, 82, 20, 86, 26, 90, 48, 94, 14, 98, 20, 102, 30, 106, 24, 110, 20, 114, 60, 118, 18, 122, 64, 126, 14, 130
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OFFSET
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1,1
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COMMENTS
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Suggested by reading Joshua Zucker's puzzle in Gary Antonick's Numberplay column for April 22 2013. Sequence A016825 gives the "primes" (the irreducible elements) in Evenland.
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LINKS
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EXAMPLE
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20 = 2*10 so a(10) = 2+10 = 12.
The first time there is a choice is when n=18: 36 = 2*18 = 6*6, and the latter gives the smaller sum, so a(18) = 6+6 = 12.
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PROG
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(PARI) f(x, i)=local(t); if(x==1, 0, if(i>#d, 2^99, t=f(x, i+1); if(x%d[i], t, min(t, d[i]+f(x/d[i], i)))))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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