

A247653


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.


2



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

1,1


COMMENTS

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.


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(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.


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(2*n)); f(2*n, 1) \\ Jens Kruse Andersen, Oct 01 2014


CROSSREFS

Cf. A016825, A247654, A001414.
Sequence in context: A159276 A056942 A115947 * A061228 A070229 A248835
Adjacent sequences: A247650 A247651 A247652 * A247654 A247655 A247656


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



