A081806 Least positive number that can be written using prime factors of n (with repetition) and the operations add and subtract.

2, 3, 4, 5, 1, 7, 2, 6, 3, 11, 1, 13, 5, 2, 4, 17, 2, 19, 1, 4, 9, 23, 1, 10, 11, 3, 3, 29, 4, 31, 2, 8, 15, 2, 2, 37, 17, 10, 1, 41, 2, 43, 7, 1, 21, 47, 1, 14, 2, 14, 9, 53, 1, 6, 1, 16, 27, 59, 2, 61, 29, 1, 4, 8, 6, 67, 13, 20, 4, 71, 2, 73, 35, 3, 15, 4, 8, 79, 1, 6, 39, 83, 4, 12, 41, 26, 5

Offset: 2

Author

Reinhard Zumkeller, Apr 10 2003

Keywords

• nonn

Comments

a(n) <= A001414(n); a(n)=A001414(n)=n iff n is prime.

Examples

			24=2*2*2*3 -> a(24) = 2-2-2+3 = 1;
30=2*3*5 -> a(30) = 2-3+5 = 4, as -2-3-5<1, -2-3+5<1, -2+3-5<1, -2+3+5>4, 2-3-5<1, 2+3-5<1 and 2+3+5>4.
		

Links

• Donovan Johnson, Table of n, a(n) for n = 2..1000

Crossrefs

Cf. A082729, A001222.

Programs

PARI

v=vector(9); for(n=2, 1000, c=0; f=factorint(n); for(j=1, omega(n), for(h=1, f[j,2], c++; v[c]=f[j,1])); nn=997; for(j=0, 2^c-1, s=0; for(h=0, c-1, if(bittest(j,h)==0, s=s-v[h+1], s=s+v[h+1])); if(s>0, if(sDonovan Johnson, Sep 14 2013 */