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

1,2

Comments

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

Links

Table of n, a(n) for n=1..90.

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).

Example

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.

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}]

Prog

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

Crossrefs

Cf. A000005, A126131.

Sequence in context: A345137 A208478 A274450 * A126131 A343332 A138012

Adjacent sequences: A366976 A366977 A366978 * A366980 A366981 A366982

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Oct 30 2023

Status

approved