A307118 a(1) = 0; for n>1, a(n) = dr(n-1) + dr(n) + dr(n+1), where dr(n) is the number of nontrivial divisors of n (A070824).

0, 0, 1, 1, 3, 2, 4, 3, 5, 3, 6, 4, 6, 4, 7, 5, 7, 4, 8, 6, 8, 4, 8, 7, 9, 5, 8, 6, 10, 6, 10, 6, 8, 6, 11, 9, 9, 4, 10, 8, 12, 6, 10, 8, 10, 6, 10, 9, 13, 7, 10, 6, 10, 8, 14, 10, 10, 4, 12, 10, 12, 6, 11, 11, 13, 8, 10, 6, 12, 8, 16, 10, 12, 6, 10, 10, 12, 8, 14, 11, 13, 5, 12, 12, 14, 6, 10, 8, 16, 12, 16

Offset: 1

Author

Todor Szimeonov, Mar 25 2019

Keywords

• nonn

Comments

Real divisibility of n's one-area (or 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 (where 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 areas, etc.

Crossrefs

Cf. A070824, A307119, A307120.

Programs

Mathematica

{0}~Join~MapAt[# + 1 &, Total /@ Partition[DivisorSigma[0, Range@ 82] - 2, 3, 1], 1] (* Michael De Vlieger, Jun 06 2019 *)

PARI

dr(n) = if (n<2, 0, numdiv(n)-2);
a(n) = if (n==1, 0, dr(n-1) + dr(n) + dr(n+1)); \\ Michel Marcus, Apr 11 2019