A062550 -id:A062550 - cp's OEIS frontend

A013942 Triangle of numbers T(n,k) = floor(2n/k), k=1..2n, read by rows.

2, 1, 4, 2, 1, 1, 6, 3, 2, 1, 1, 1, 8, 4, 2, 2, 1, 1, 1, 1, 10, 5, 3, 2, 2, 1, 1, 1, 1, 1, 12, 6, 4, 3, 2, 2, 1, 1, 1, 1, 1, 1, 14, 7, 4, 3, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 16, 8, 5, 4, 3, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 18, 9, 6, 4, 3, 3, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 20, 10, 6, 5, 4, 3

Offset: 1

Clark Kimberling

a(n) is also the leading term in period of continued fraction for n-th nonsquare.

Row A026741(n) contains n and all rows with a smaller row number do not contain n. - Reinhard Zumkeller, Jun 04 2013

			First four rows:
  2 1
  4 2 1 1
  6 3 2 1 1 1
  8 4 2 2 1 1 1 1
  ...

Reinhard Zumkeller, Rows n = 1..100 of table, flattened

Cf. A010766.

Cf. A005843 (row lengths and left edge), A062550 (row sums).

a013942 n k = a013942_tabf !! (n-1) !! (k-1)
a013942_row n = map (div (n * 2)) [1 .. 2 * n]
a013942_tabf = map a013942_row [1 ..]
-- Reinhard Zumkeller, Jun 04 2013

f[n_,h_]:=FractionalPart[(n^2+h)^(1/2)];
g[n_,h_]:=Floor[1/f[n,h]];
TableForm[Table[g[n,h],{n,1,13},{h,1,2n}]]

T(n, k) = 2*n\k;
tabf(nn) = for (n=1, nn, for (k=1, 2*n, print1(T(n,k), ", ")); print()); \\ Michel Marcus, Sep 30 2016

T(n,k) = floor(2n/k), k=1,...,2n.

T(n,k) = [1/{sqrt(k+n^2)}], k=1,2,...,2n, {}=fractional part, []=floor.

Keyword tabl replaced by tabf and missing a(90)=1 inserted by Reinhard Zumkeller, Jun 04 2013

A158568 a(n) = Sum_{i=1..Fibonacci(n)} sigma_0(i) where sigma_0(n) is A000005(n).

Original entry on oeis.org

1, 1, 3, 5, 10, 20, 37, 70, 127, 231, 413, 746, 1307, 2295, 4010, 6957, 12031, 20712, 35514, 60718, 103500, 175989, 298539, 505399, 853777, 1439856, 2424299, 4075479, 6841787, 11470592, 19207624, 32126763, 53678285

Offset: 1

Ctibor O. Zizka, Mar 21 2009

nonn

Chai Wah Wu, Table of n, a(n) for n = 1..106

Cf. A000005, A000045, A006218, A085831, A062550, A153876, A153817, A153816.

with(combinat):with(numtheory): A158568 := proc(n) return add(tau(i),i=1..fibonacci(n)): end: seq(A158568(n),n=1..20); # Nathaniel Johnston, May 09 2011

Module[{nn=33,f,d},f=Fibonacci[nn];d=DivisorSigma[0,Range[f]];Table[ Total[ Take[d,n]],{n,Fibonacci[Range[nn]]}]] (* Harvey P. Dale, Apr 29 2018 *)

a(n) = sum(k=1, fibonacci(n), numdiv(k)); \\ Michel Marcus, Feb 12 2019

from math import isqrt
def A153568(n):
    a, b, = 0, 1
    for _ in range(n): a, b = b, a+b
    return (lambda m: 2*sum(a//k for k in range(1, m+1))-m*m)(isqrt(a)) # Chai Wah Wu, Oct 09 2021

a(16)-a(33) from Nathaniel Johnston, May 09 2011

cp's OEIS Frontend

A013942 Triangle of numbers T(n,k) = floor(2n/k), k=1..2n, read by rows.

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