A307119 -id:A307119 - cp's OEIS frontend

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

Todor Szimeonov, Mar 25 2019

nonn

(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.

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

Cf. A000005, A307118, A307119.

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

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

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).

Original entry on oeis.org

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

Todor Szimeonov, Mar 25 2019

nonn

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.

Cf. A070824, A307119, A307120.

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

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

cp's OEIS Frontend

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

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