A006591 a(n) = Sum_{k=1..n} nearest integer to n/k (if n/k is midway between two numbers take the smaller). (Formerly M2434)

1, 3, 5, 8, 11, 14, 17, 22, 24, 28, 33, 36, 40, 45, 48, 53, 57, 62, 66, 71, 74, 79, 86, 89, 93, 99, 102, 109, 114, 117, 122, 129, 133, 138, 143, 148, 152, 159, 164, 169, 175, 178, 185, 190, 193, 202, 207, 212, 215, 223, 227, 232, 241, 244, 249, 256, 259, 266, 273

Offset

1,2

Comments

Number of ways the numbers from 1..n divide the numbers from n..2n-1, n>=2. - Wesley Ivan Hurt, Feb 08 2022

References

Marc LeBrun, personal communication.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Table of n, a(n) for n=1..59.

M. Le Brun, Email to N. J. A. Sloane, Jul 1991

Formula

a(n) = n^2 - Sum_{k=1..n} Sum_{i=n..2n-1} sign(i mod k). - Wesley Ivan Hurt, Feb 08 2022

Example

a(3) = 3 + 1 + 1 = 5. a(7) = 17 = 7 + 3 + 2 + 2 + 1 + 1 + 1.

Mathematica

rnd[n_] := If[Mod[n, 1] > .5, Ceiling[n], Floor[n]]; Table[ Sum[ rnd[ n/k], {k, 1, n} ], {n, 1, 70} ]

Crossrefs

Cf. A006218.

Sequence in context: A278586 A001855 A377410 * A310027 A310028 A287414

Adjacent sequences: A006588 A006589 A006590 * A006592 A006593 A006594

Keyword

nonn,easy

Author

N. J. A. Sloane.

Extensions

More terms from Robert G. Wilson v, Oct 22 2001

Status

approved