A056549 -id:A056549 - cp's OEIS frontend

A062550 a(n) = Sum_{k = 1..2n} floor(2n/k).

0, 3, 8, 14, 20, 27, 35, 41, 50, 58, 66, 74, 84, 91, 101, 111, 119, 127, 140, 146, 158, 168, 176, 186, 198, 207, 217, 227, 239, 247, 261, 267, 280, 292, 300, 312, 326, 332, 344, 356, 368, 377, 391, 399, 411, 425, 435, 443, 459, 467, 482, 492, 502, 514, 528

Offset: 0

Henry Bottomley, Jun 26 2001

nonn

The sequence A006218 : Sum_{i=1..n} floor(n/i) = Sum_{i=1..n} sigma_0(i). Sigma_0(i) is A000005. Sequences of the type : Sum_{i=1..f(n)} floor(f(n)/i)= Sum_{i=1..f(n)} sigma_0(i). This sequence a(n)= A006218(2*n). [Ctibor O. Zizka, Mar 21 2009]

For n > 0: row sums of the triangle in A013942. - Reinhard Zumkeller, Jun 04 2013

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Cf. A013942, A156745, A085831, A153816, A153817, A153876.

a062550 0 = 0
a062550 n = sum $ a013942_row n  -- Reinhard Zumkeller, Jun 04 2013

Table[Total[Floor[2*n/Range[2*n]]], {n, 0, 100}] (* T. D. Noe, Jun 12 2013 *)

a(n) = sum(k=1, 2*n, (2*n)\k); \\ Michel Marcus, Oct 09 2021

from math import isqrt
def A062550(n): return (lambda m: 2*sum(2*n//k for k in range(1, m+1))-m*m)(isqrt(2*n)) # Chai Wah Wu, Oct 09 2021

a(n) = A006218(2n) = A056549(n)+A006218(n) = a(n-1)+A000005(2n-1)+A000005(2n)

Data corrected for n > 30 by Reinhard Zumkeller, Jun 04 2013

A056548 a(n) = Sum_{k>=1} round(n/k) where round(1/2) = 0.

Original entry on oeis.org

0, 1, 4, 7, 11, 15, 19, 23, 29, 32, 37, 43, 47, 52, 58, 62, 68, 73, 79, 84, 90, 94, 100, 108, 112, 117, 124, 128, 136, 142, 146, 152, 160, 165, 171, 177, 183, 188, 196, 202, 208, 215, 219, 227, 233, 237, 247, 253, 259, 263, 272, 277, 283, 293, 297, 303, 311, 315

Offset: 0

Henry Bottomley, Jun 21 2000

Cf. A000005, A001227, A006218, A056549.

a(n) = A056549(n) - A001227(n).

Conjecture: a(n) = Sum_{k=n..2n-1} d(k), where d is the number of divisors function (A000005). - Ridouane Oudra, Apr 29 2019

A211707 Rectangular array: R(n,k)=n+[n/2+1/2]+...+[n/k+1/2], where [ ]=floor and k>=1, by antidiagonals.

Original entry on oeis.org

1, 2, 2, 3, 3, 2, 4, 5, 4, 2, 5, 6, 6, 5, 2, 6, 8, 7, 7, 5, 2, 7, 9, 10, 8, 8, 5, 2, 8, 11, 11, 11, 9, 9, 5, 2, 9, 12, 13, 13, 12, 10, 9, 5, 2, 10, 14, 15, 15, 14, 13, 11, 9, 5, 2, 11, 15, 17, 17, 16, 15, 14, 12, 9, 5, 2, 12, 17, 18, 19, 19, 17, 16, 15, 12, 9, 5, 2, 13, 18, 21

Offset: 1

Clark Kimberling, Apr 20 2012

Limit of n-th row:  A056549=(2,5,9,12,17,21,25,...).
Row 1:  A000027
Row 2:  A007494
R(n,n)=A077024(n)
For n>=1, row n is a homogeneous linear recurrence sequence of order A005728(n) with palindromic recurrence coefficients in the sense described at A211701.

			Northwest corner:
1...2...3...4...5....6....7
2...3...5...6...8....9....11
2...4...6...7...10...11...12
2...5...7...8...11...13...15
2...5...8...9...12...14...16

Cf. A211701

f[n_, m_] := Sum[Floor[n/k + 1/2], {k, 1, m}]
TableForm[Table[f[n, m], {m, 1, 20}, {n, 1, 16}]]

cp's OEIS Frontend

A062550 a(n) = Sum_{k = 1..2n} floor(2n/k).

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A056548 a(n) = Sum_{k>=1} round(n/k) where round(1/2) = 0.

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A211707 Rectangular array: R(n,k)=n+[n/2+1/2]+...+[n/k+1/2], where [ ]=floor and k>=1, by antidiagonals.

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