

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.


2



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
(list;
graph;
refs;
listen;
history;
text;
internal format)



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



