A082729 Least positive number that can be written using all divisors of n and the operations add and subtract.

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, 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, 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

Offset

1,3

Comments

a(n) < A000203(n); a(n)=A000010(n)=n-1 iff n is prime or n=6;

a(2^n)=1, a(A000079(n))=1.

Links

Donovan Johnson, Table of n, a(n) for n = 1..1000

Example

Divisors of n=18: {1,2,3,6,9,18} -> a(18)=-1+2-3-6-9+18=1.
Divisors of n=15: {1,3,5,15} -> a(15)=-1-3-5+15=6, as
-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,
-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,
1-3+5+15>6, -1+3+5+15>6 and 1+3+5+15>6.

Prog

(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 */

Crossrefs

Cf. A081806, A000005.

Sequence in context: A125131 A003958 A326140 * A326069 A326068 A318878

Adjacent sequences: A082726 A082727 A082728 * A082730 A082731 A082732

Keyword

nonn

Author

Reinhard Zumkeller, Apr 13 2003

Status

approved