A307120 a(1) = 3, for n>1, a(n) = A000005(n-1) + A000005(n) + A000005(n+1).

3, 5, 7, 7, 9, 8, 10, 9, 11, 9, 12, 10, 12, 10, 13, 11, 13, 10, 14, 12, 14, 10, 14, 13, 15, 11, 14, 12, 16, 12, 16, 12, 14, 12, 17, 15, 15, 10, 16, 14, 18, 12, 16, 14, 16, 12, 16, 15, 19, 13, 16, 12, 16, 14, 20, 16, 16, 10, 18, 16, 18, 12, 17, 17, 19, 14, 16, 12, 18, 14, 22, 16, 18, 12, 16, 16, 18, 14, 20

Offset: 1

Author

Todor Szimeonov, Mar 25 2019

Keywords

• nonn

Comments

(Tau) divisibility of n's 1-area. This is the first step to examine the divisibility of n's k-area. n's k-area is the set of m for which |n-m| is less than or equal to k (n, k, m are natural numbers). 1's 1-area is {1,2}, 5's 1-area {4,5,6}, 3's 2-area {1,2,3,4,5}. We could call this natural area, and still talk about nonnegative or integer area etc.

Examples

			a(10) = 9 as 9 has 3 divisors, 10 has 4 divisors and 11 has 2 divisors. - _David A. Corneth_, Mar 26 2019
		

Crossrefs

Cf. A000005, A307118, A307119.

Programs

Mathematica

{3}~Join~Map[Total, Partition[DivisorSigma[0, Range@ 80], 3, 1]] (* Michael De Vlieger, Jun 06 2019 *)

PARI

a(n) = if(n == 3, return(1)); sum(i = n-1, n+1, numdiv(i)) \\ David A. Corneth, Mar 26 2019