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%I #8 Sep 14 2013 17:43:51
%S 1,1,2,1,4,2,6,1,5,2,10,2,12,4,6,1,16,1,18,2,10,8,22,2,19,10,14,2,28,
%T 2,30,1,18,14,22,1,36,16,22,2,40,2,42,4,12,20,46,2,41,7,30,6,52,2,38,
%U 2,34,26,58,2,60,28,22,1,46,2,66,10,42,2,70,1,72,34,26,12,58,2,78,2,41,38,82
%N Least positive number that can be written using all divisors of n and the operations add and subtract.
%C a(n) < A000203(n); a(n)=A000010(n)=n-1 iff n is prime or n=6;
%C a(2^n)=1, a(A000079(n))=1.
%H Donovan Johnson, <a href="/A082729/b082729.txt">Table of n, a(n) for n = 1..1000</a>
%e Divisors of n=18: {1,2,3,6,9,18} -> a(18)=-1+2-3-6-9+18=1.
%e Divisors of n=15: {1,3,5,15} -> a(15)=-1-3-5+15=6, as
%e -1-3-5-15<1, 1-3-5-15<1, -1+3-5-15<1, 1+3-5-15<1, -1-3+5-15<1, 1-3+5-15<1,
%e -1+3+5-15<1, 1+3+5-15<1, 1-3-5+15>6, -1+3-5+15>6, 1+3-5+15>6, -1-3+5+15>6,
%e 1-3+5+15>6, -1+3+5+15>6 and 1+3+5+15>6.
%o (PARI) for(n=1, 1000, nd=numdiv(n); d=divisors(n); nn=3048; for(j=0, 2^nd-1, s=0; for(h=0, nd-1, if(bittest(j,h)==0, s=s-d[h+1], s=s+d[h+1])); if(s>0, if(s<nn, nn=s))); write("b082729.txt", n " " nn)) /* _Donovan Johnson_, Sep 14 2013 */
%Y Cf. A081806, A000005.
%K nonn
%O 1,3
%A _Reinhard Zumkeller_, Apr 13 2003
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