A307119 a(1) = 1, for n>1, a(n) = dp(n-1) + dp(n) + dp(n+1), where dp(n) is the number of divisors of n less than n (A032741).

1, 2, 4, 4, 6, 5, 7, 6, 8, 6, 9, 7, 9, 7, 10, 8, 10, 7, 11, 9, 11, 7, 11, 10, 12, 8, 11, 9, 13, 9, 13, 9, 11, 9, 14, 12, 12, 7, 13, 11, 15, 9, 13, 11, 13, 9, 13, 12, 16, 10, 13, 9, 13, 11, 17, 13, 13, 7, 15, 13, 15, 9, 14, 14, 16, 11, 13, 9, 15, 11, 19, 13, 15, 9, 13, 13, 15, 11, 17, 14, 16, 8

Offset: 1

Author

Todor Szimeonov, Mar 25 2019

Keywords

• nonn

Comments

Proper 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 areas etc.

Crossrefs

Cf. A032741, A307118, A307120.

Programs

Mathematica

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

PARI

dp(n) = if (n < 1, 0, numdiv(n) - 1);
a(n) = dp(n-1) + dp(n) + dp(n+1); \\ Michel Marcus, Jun 11 2019