A109046 -id:A109046 - cp's OEIS frontend

A060791 a(n) = n / gcd(n,5).

1, 2, 3, 4, 1, 6, 7, 8, 9, 2, 11, 12, 13, 14, 3, 16, 17, 18, 19, 4, 21, 22, 23, 24, 5, 26, 27, 28, 29, 6, 31, 32, 33, 34, 7, 36, 37, 38, 39, 8, 41, 42, 43, 44, 9, 46, 47, 48, 49, 10, 51, 52, 53, 54, 11, 56, 57, 58, 59, 12, 61, 62, 63, 64, 13, 66, 67, 68, 69

Offset: 1

Len Smiley, Apr 26 2001

As well as being a multiplicative sequence, a(n) is also strong divisibility sequence, that is, gcd(a(n),a(m)) = a(gcd(n,m)) for n, m >= 1. In particular, a(n) is a divisibility sequence: if n divides m then a(n) divides a(m). Peter Bala, Feb 20 2019

Harry J. Smith, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,2,0,0,0,0,-1).

Cf. Sequences given by the formula n/gcd(n,k) = numerator(n/(n + k)): A026741 (k = 2), A051176 (k = 3), A060819 (k = 4), A060789 (k = 6), A106608 thru A106612 (k = 7 thru 11), A051724 (k = 12), A106614 thru A106621 (k = 13 thru 20).

Cf. A109046.

List([1..80],n->n/Gcd(n,5)); # Muniru A Asiru, Feb 20 2019

[n/GCD(n, 5): n in [1..100]]; // G. C. Greubel, Feb 20 2019

seq(n/gcd(n,5),n=1..80); # Muniru A Asiru, Feb 20 2019

f[n_]:=Numerator[n/(n+5)]; Array[f,100] (* Vladimir Joseph Stephan Orlovsky, Feb 16 2011*)

a(n) = { n / gcd(n, 5) } \\ Harry J. Smith, Jul 12 2009

a(n) = n/(5-4*(n%5>0)) \\ Zak Seidov, Feb 17 2011

[lcm(n,5)/5 for n in range(1, 51)] # Zerinvary Lajos, Jun 07 2009

G.f.: x*(1 + 2*x + 3*x^2 + 4*x^3 + x^4 + 4*x^5 + 3*x^6 + 2*x^7 + x^8)/(1 - x^5)^2.
a(n) = n/5 if 5|n, otherwise a(n) = n.
From R. J. Mathar, Apr 18 2011: (Start)
a(n) = A109046(n)/5.
Dirichlet g.f.: zeta(s-1)*(1-4/5^s). (End)
G.f.: x*(x^4 + x^3 - x^2 + x + 1)*(x^4 + x^3 + 3*x^2 + x + 1)/((x - 1)^2*(x^4 + x^3 + x^2 + x + 1)^2). - R. J. Mathar, Oct 31 2015
From Peter Bala, Feb 20 2019: (Start)
a(n) = numerator(n/(n + 5)).
If gcd(n, m) = 1 then a(a(n)*a(m)) = a(a(n)) * a(a(m)), a(a(a(n))*a(a(m))) = a(a(a(n))) * a(a(a(m))) and so on.
G.f.: x/(1 - x)^2 - 4*x^5/(1 - x^5)^2. (End)
Sum_{k=1..n} a(k) ~ (21/50) * n^2. - Amiram Eldar, Nov 25 2022
Sum_{n>=1} (-1)^(n+1)/a(n) = 9*log(2)/5. - Amiram Eldar, Sep 08 2023

Extended (using terms from b-file) by Michel Marcus, Feb 08 2014

A109042 Square array read by antidiagonals: A(n, k) = lcm(n, k) for n >= 0, k >= 0.

Original entry on oeis.org

0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 0, 3, 2, 3, 0, 0, 4, 6, 6, 4, 0, 0, 5, 4, 3, 4, 5, 0, 0, 6, 10, 12, 12, 10, 6, 0, 0, 7, 6, 15, 4, 15, 6, 7, 0, 0, 8, 14, 6, 20, 20, 6, 14, 8, 0, 0, 9, 8, 21, 12, 5, 12, 21, 8, 9, 0, 0, 10, 18, 24, 28, 30, 30, 28, 24, 18, 10, 0, 0, 11, 10, 9, 8, 35, 6, 35, 8, 9, 10, 11, 0

Offset: 0

Mitch Harris, Jun 18 2005

			Seen as an array:
  [0] 0, 0,  0,  0,  0,  0,  0,  0,  0,  0, ...
  [1] 0, 1,  2,  3,  4,  5,  6,  7,  8,  9, ...
  [2] 0, 2,  2,  6,  4, 10,  6, 14,  8, 18, ...
  [3] 0, 3,  6,  3, 12, 15,  6, 21, 24,  9, ...
  [4] 0, 4,  4, 12,  4, 20, 12, 28,  8, 36, ...
  [5] 0, 5, 10, 15, 20,  5, 30, 35, 40, 45, ...
  [6] 0, 6,  6,  6, 12, 30,  6, 42, 24, 18, ...
  [7] 0, 7, 14, 21, 28, 35, 42,  7, 56, 63, ...
  [8] 0, 8,  8, 24,  8, 40, 24, 56,  8, 72, ...
  [9] 0, 9, 18,  9, 36, 45, 18, 63, 72,  9, ...
.
Seen as a triangle T(n, k) = lcm(n - k, k).
  [0] 0;
  [1] 0, 0;
  [2] 0, 1,  0;
  [3] 0, 2,  2,  0;
  [4] 0, 3,  2,  3,  0;
  [5] 0, 4,  6,  6,  4,  0;
  [6] 0, 5,  4,  3,  4,  5, 0;
  [7] 0, 6, 10, 12, 12, 10, 6,  0;
  [8] 0, 7,  6, 15,  4, 15, 6,  7, 0;
  [9] 0, 8, 14,  6, 20, 20, 6, 14, 8, 0;

Alois P. Heinz, Antidiagonals n = 0..140, flattened

Rows A000027, A109043, A109044, A109045, A109046, A109047, A109048, A109049, A109050, A109051, A109052, A109053, A006580 (row sums of triangle), A001477 (main diagonal, central terms).

Variants: A003990 is (1, 1) based, A051173 (T(n,k) = lcm(n,k)).

T := (n, k) -> ilcm(n - k, k):
for n from 0 to 9 do seq(T(n, k), k = 0..n) od;  # Peter Luschny, Mar 24 2025

lcm(n, k) = n*k / gcd(n, k) for (n, k) != (0, 0).

A283442 a(n) = lcm(n,5) / gcd(n,5).

Original entry on oeis.org

0, 5, 10, 15, 20, 1, 30, 35, 40, 45, 2, 55, 60, 65, 70, 3, 80, 85, 90, 95, 4, 105, 110, 115, 120, 5, 130, 135, 140, 145, 6, 155, 160, 165, 170, 7, 180, 185, 190, 195, 8, 205, 210, 215, 220, 9, 230, 235, 240, 245, 10, 255, 260, 265, 270, 11, 280, 285, 290

Offset: 0

Colin Barker, Mar 07 2017

Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,2,0,0,0,0,-1).

Cf. A064680, A130724, A188134, A283443, A283444.

Cf. A109009, A109046.

Table[LCM[n, 5] / GCD[n, 5], {n,0,58}] (* Indranil Ghosh, Mar 08 2017 *)
LinearRecurrence[{0,0,0,0,2,0,0,0,0,-1},{0,5,10,15,20,1,30,35,40,45},60] (* Harvey P. Dale, Aug 11 2019 *)

concat(0, Vec(x*(5 + 10*x + 15*x^2 + 20*x^3 + x^4 + 20*x^5 + 15*x^6 + 10*x^7 + 5*x^8) / ((1 - x)^2*(1 + x + x^2 + x^3 + x^4)^2) + O(x^100)))

{for (n=0, 58, print1((lcm(n, 5) / gcd(n, 5)),", "))}; \\ Indranil Ghosh, Mar 08 2017

G.f.: x*(5 + 10*x + 15*x^2 + 20*x^3 + x^4 + 20*x^5 + 15*x^6 + 10*x^7 + 5*x^8) / ((1 - x)^2*(1 + x + x^2 + x^3 + x^4)^2).
a(n) = A109046(n) / A109009(n).
a(n) = 2*a(n-5) - a(n-10) for n>9.
Sum_{k=1..n} a(k) ~ (101/50)*n^2. - Amiram Eldar, Oct 07 2023

cp's OEIS Frontend

A060791 a(n) = n / gcd(n,5).

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A109042 Square array read by antidiagonals: A(n, k) = lcm(n, k) for n >= 0, k >= 0.

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A283442 a(n) = lcm(n,5) / gcd(n,5).

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