A366979 Number of divisors of n less than or equal to d(n).

1, 2, 1, 2, 1, 3, 1, 3, 2, 2, 1, 5, 1, 2, 2, 3, 1, 4, 1, 4, 2, 2, 1, 6, 1, 2, 2, 3, 1, 5, 1, 3, 2, 2, 1, 6, 1, 2, 2, 5, 1, 5, 1, 3, 3, 2, 1, 6, 1, 3, 2, 3, 1, 4, 1, 5, 2, 2, 1, 8, 1, 2, 2, 3, 1, 4, 1, 3, 2, 4, 1, 8, 1, 2, 3, 3, 1, 4, 1, 6, 2, 2, 1, 7, 1, 2, 2, 4, 1, 7

Offset: 1

Author

Wesley Ivan Hurt, Oct 30 2023

Keywords

• nonn
• easy

Comments

First differs from A126131 at a(25) = 1.

Examples

			a(8) = 3; There are 3 divisors of 8 that are <= d(8) = 4.  They are: {1,2,4}.
a(25) = 1; 1 is the only divisor of 25 that is <= d(25) = 3.
		

Crossrefs

Cf. A000005, A126131.

Programs

Mathematica

Table[1 + Sum[Sum[(Sign[Floor[i/k]] - Sign[Floor[(i - 1)/k]]), {i, 2, DivisorSigma[0, n]}] (1 - Ceiling[n/k] + Floor[n/k]), {k, n}], {n, 100}]

PARI

a(n) = my(nd=numdiv(n)); sumdiv(n, d, d <= nd); \\ Michel Marcus, Oct 30 2023

Formula

a(n) = Sum_{d|n, d <= d(n)} 1.

a(n) = 1 + Sum_{d|n} (Sum_{i=2..d(n)} ( sign(floor(i/d)) - sign(floor((i-1)/d)) )), where d(n) is the number of divisors of n (A000005).