A156745 -id:A156745 - 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

A334954 a(n) is 1 plus the number of divisors of n.

Original entry on oeis.org

2, 3, 3, 4, 3, 5, 3, 5, 4, 5, 3, 7, 3, 5, 5, 6, 3, 7, 3, 7, 5, 5, 3, 9, 4, 5, 5, 7, 3, 9, 3, 7, 5, 5, 5, 10, 3, 5, 5, 9, 3, 9, 3, 7, 7, 5, 3, 11, 4, 7, 5, 7, 3, 9, 5, 9, 5, 5, 3, 13, 3, 5, 7, 8, 5, 9, 3, 7, 5, 9, 3, 13, 3, 5, 7, 7, 5, 9, 3, 11, 6, 5, 3, 13, 5, 5, 5, 9, 3, 13, 5, 7, 5, 5, 5, 13, 3, 7, 7, 10, 3, 9, 3, 9

Offset: 1

David A. Corneth and Omar E. Pol, Aug 25 2020

a(n) is the number of times that every divisor of n occurs in the coordinates of divisors of n mentioned in A337360 (Corneth).
a(n) = 3 if and only if n is prime.
a(n) is even if and only if n is a square.
a(n) is the number of characteristic subgroups of the dihedral group D_2n. - Firdous Ahmad Mala, Dec 25 2021

David A. Corneth, Table of n, a(n) for n = 1..10000

Partial sums give A156745.

Cf. A000005, A088580, A000203, A212356, A337360.

1 + DivisorSigma[0, Range[105]] (* Michael De Vlieger, Sep 11 2020 *)

PARI
```
a(n) = numdiv(n) + 1
```

a(n) = 1 + A000005(n).
a(n) = A337360(n)/A000203(n).
a(n) = A212356(n) for n >= 3. - Ilya Gutkovskiy, Aug 27 2020

cp's OEIS Frontend

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

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