A247654 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.

4, 6, 8, 8, 12, 10, 16, 10, 12, 14, 24, 12, 28, 18, 16, 12, 36, 14, 40, 16, 20, 26, 48, 14, 20, 30, 24, 20, 60, 18, 64, 14, 28, 38, 24, 16, 76, 42, 32, 18, 84, 22, 88, 28, 28, 50, 96, 16, 28, 22, 40, 32, 108, 18, 32, 22, 44, 62, 120, 20, 124, 66, 32, 16, 36

Offset

1,1

Comments

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

Links

Jens Kruse Andersen, Table of n, a(n) for n = 1..10000

Gary Antonick, The Primes in Evenland Puzzle, Numberplay Column, Wordplay Blog, New York Times, April 22, 2013

Example

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

Prog

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

Crossrefs

Cf. A016825, A001414. A bisection of A247653.

Sequence in context: A027709 A196358 A079775 * A262767 A104173 A023991

Adjacent sequences: A247651 A247652 A247653 * A247655 A247656 A247657

Keyword

nonn

Author

N. J. A. Sloane, Sep 30 2014

Extensions

Definition corrected and more terms from Jens Kruse Andersen, Oct 01 2014

Status

approved