A141501 a(n) is smallest integer for which the number of integers from 1 to a(n) that are not divisors of n is greater than the number of integers from 1 to a(n) that are divisors of n.

3, 5, 5, 7, 3, 9, 3, 7, 5, 7, 3, 11, 3, 5, 7, 7, 3, 11, 3, 9, 5, 5, 3, 15, 3, 5, 5, 9, 3, 13, 3, 7, 5, 5, 3, 15, 3, 5, 5, 13, 3, 11, 3, 7, 7, 5, 3, 15, 3, 7, 5, 7, 3, 11, 3, 11, 5, 5, 3, 19, 3, 5, 5, 7, 3, 9, 3, 7, 5, 9, 3, 17, 3, 5, 7, 7, 3, 9, 3, 13, 5, 5, 3, 17, 3, 5, 5, 7, 3, 17, 3, 7, 5, 5, 3, 15, 3, 5

Offset

1,1

Comments

Is a(n) always odd?

Yes, a(n) is always odd. At a(n) - 1, there are the same number of divisors and non-divisors, so a(n) - 1 is even. - Franklin T. Adams-Watters, Feb 09 2018

Links

Table of n, a(n) for n=1..98.

Example

a(6) = 9 because among the integers 1 through 9 we have:
Divisors: 1, 2, 3, 6;
Non-divisors: 4, 5, 7, 8, 9.

Prog

(PARI) {for(n=1, 100, k=1; d=divisors(n); while(1, c=0; for(j=1, #d, if(d[j]<=k, c++)); if(k-c<=c, k++, break)); print1(k, ", "))} \\ Klaus Brockhaus, Aug 18 2008

Crossrefs

Cf. A143474 (smallest k such that A141501(k) = 2*n+1). - Klaus Brockhaus, Aug 25 2008

Sequence in context: A266567 A282624 A179858 * A277776 A103988 A285204

Adjacent sequences: A141498 A141499 A141500 * A141502 A141503 A141504

Keyword

nonn

Author

J. Lowell, Aug 10 2008

Extensions

Extended by Klaus Brockhaus, Aug 18 2008

Status

approved