%I #14 Oct 02 2014 23:17:25

%S 4,6,8,8,12,10,16,10,12,14,24,12,28,18,16,12,36,14,40,16,20,26,48,14,

%T 20,30,24,20,60,18,64,14,28,38,24,16,76,42,32,18,84,22,88,28,28,50,96,

%U 16,28,22,40,32,108,18,32,22,44,62,120,20,124,66,32,16,36

%N Write 4n 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.

%C Suggested by reading Joshua Zucker's puzzle in Gary Antonick's Numberplay column for April 22 2013.

%H Jens Kruse Andersen, <a href="/A247654/b247654.txt">Table of n, a(n) for n = 1..10000</a>

%H Gary Antonick, <a href="http://wordplay.blogs.nytimes.com/2013/04/22/evenland/">The Primes in Evenland Puzzle</a>, Numberplay Column, Wordplay Blog, New York Times, April 22, 2013

%e 20 = 2*10 so a(5) = 2+10 = 12.

%e The first time there is a choice is when n=9: 36 = 2*18 = 6*6, and the latter gives the smaller sum, so a(9) = 6+6 = 12.

%o (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)))))

%o a(n)=d=select(m->m%4==2, divisors(4*n)); f(4*n, 1) \\ _Jens Kruse Andersen_, Oct 01 2014

%Y Cf. A016825, A001414. A bisection of A247653.

%K nonn

%O 1,1

%A _N. J. A. Sloane_, Sep 30 2014

%E Definition corrected and more terms from _Jens Kruse Andersen_, Oct 01 2014