A188134 -id:A188134 - cp's OEIS frontend

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

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

A283443 a(n) = lcm(n,6) / gcd(n,6).

Original entry on oeis.org

0, 6, 3, 2, 6, 30, 1, 42, 12, 6, 15, 66, 2, 78, 21, 10, 24, 102, 3, 114, 30, 14, 33, 138, 4, 150, 39, 18, 42, 174, 5, 186, 48, 22, 51, 210, 6, 222, 57, 26, 60, 246, 7, 258, 66, 30, 69, 282, 8, 294, 75, 34, 78, 318, 9, 330, 84, 38, 87, 354, 10, 366, 93, 42

Offset: 0

Colin Barker, Mar 07 2017

If n == 2 or 4 (mod 6) then a(n) = 3*n/2; if n == 3 (mod 6) then a(n) = 2*n/3; if n == 1 or 5 (mod 6) then a(n) = 6*n; otherwise, a(n) = n/6. Examples: n = 50 = 6*8+2, a(50) = 3*50/2 = 75; n = 23 = 6*3+5, a(23) = 6*23 = 138. - Bruno Berselli, Mar 08 2017

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

Cf. A064680, A130724, A188134, A283442, A283444.

Table[LCM[n, 6] / GCD[n, 6], {n,0,63}] (* Indranil Ghosh, Mar 08 2017 *)

concat(0, Vec(x*(6 + 3*x + 2*x^2 + 6*x^3 + 30*x^4 + x^5 + 30*x^6 + 6*x^7 + 2*x^8 + 3*x^9 + 6*x^10) / ((1 - x)^2*(1 + x)^2*(1 - x + x^2)^2*(1 + x + x^2)^2) + O(x^100)))

{for (n=0, 63, print1((lcm(n, 6) / gcd(n, 6)),", "))}; \\ Indranil Ghosh, Mar 08 2017

G.f.: x*(6 + 3*x + 2*x^2 + 6*x^3 + 30*x^4 + x^5 + 30*x^6 + 6*x^7 + 2*x^8 + 3*x^9 + 6*x^10) / ((1 - x)^2*(1 + x)^2*(1 - x + x^2)^2*(1 + x + x^2)^2).
a(n) = 2*a(n-6) - a(n-12) for n>11.
a(n) = A109047(n)/A089128(n). - R. J. Mathar, Feb 12 2019
Sum_{k=1..n} a(k) ~ (95/72)*n^2. - Amiram Eldar, Oct 07 2023

A070293 a(n) = lcm(30,n)/gcd(30,n).

Original entry on oeis.org

30, 15, 10, 30, 6, 5, 210, 60, 30, 3, 330, 10, 390, 105, 2, 120, 510, 15, 570, 6, 70, 165, 690, 20, 30, 195, 90, 210, 870, 1, 930, 240, 110, 255, 42, 30, 1110, 285, 130, 12, 1230, 35, 1290, 330, 6, 345, 1410, 40, 1470, 15

Offset: 1

Amarnath Murthy, May 10 2002

Cf. A130724, A188134, A283442, A283443, A070290, A070291, A070292.

Table[LCM[30,n]/GCD[30,n],{n,50}]  (* Harvey P. Dale, Apr 17 2011 *)

Sum_{k=1..n} a(k) ~ (1919/360)*n^2. - Amiram Eldar, Oct 07 2023

More terms from Harvey P. Dale, Apr 17 2011

A283444 a(n) = lcm(n,7) / gcd(n,7).

Original entry on oeis.org

0, 7, 14, 21, 28, 35, 42, 1, 56, 63, 70, 77, 84, 91, 2, 105, 112, 119, 126, 133, 140, 3, 154, 161, 168, 175, 182, 189, 4, 203, 210, 217, 224, 231, 238, 5, 252, 259, 266, 273, 280, 287, 6, 301, 308, 315, 322, 329, 336, 7, 350, 357, 364, 371, 378, 385, 8, 399

Offset: 0

Colin Barker, Mar 07 2017

Similar to row 7 of A059897. Apart from the extra a(0) = 0, differs first at a(49) = 7 <> 343 = A059897(7,49). Note that a(1) = 7 also, whereas all rows of A059897 are permutations of the positive integers. - Peter Munn, Jan 16 2020

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

Cf. A059897, A064680, A130724, A188134, A283442, A283443.

Table[LCM[n, 7] / GCD[n, 7], {n,0,57}] (* Indranil Ghosh, Mar 08 2017 *)
LinearRecurrence[{0,0,0,0,0,0,2,0,0,0,0,0,0,-1},{0,7,14,21,28,35,42,1,56,63,70,77,84,91},60] (* Harvey P. Dale, Apr 05 2018 *)

concat(0, Vec(x*(7 + 14*x + 21*x^2 + 28*x^3 + 35*x^4 + 42*x^5 + x^6 + 42*x^7 + 35*x^8 + 28*x^9 + 21*x^10 + 14*x^11 + 7*x^12) / ((1 - x)^2*(1 + x + x^2 + x^3 + x^4 + x^5 + x^6)^2) + O(x^100)))

{for (n=0, 57, print1((lcm(n, 7) / gcd(n, 7)),", "))}; \\ Indranil Ghosh, Mar 08 2017

G.f.: x*(7 + 14*x + 21*x^2 + 28*x^3 + 35*x^4 + 42*x^5 + x^6 + 42*x^7 + 35*x^8 + 28*x^9 + 21*x^10 + 14*x^11 + 7*x^12) / ((1 - x)^2*(1 + x + x^2 + x^3 + x^4 + x^5 + x^6)^2).
a(n) = 2*a(n-7) - a(n-14) for n > 13.
a(n) = 7^(-(m^6 - 21*m^5 + 175*m^4 - 735*m^3 + 1624*m^2 - 1764*m + 360)/360)*n where m = (n mod 7). - Luce ETIENNE, Nov 18 2019
Sum_{k=1..n} a(k) ~ (295/98)*n^2. - Amiram Eldar, Oct 07 2023

A247004 Denominator of (n+4)/gcd(n, 4)^2, a 16-periodic sequence that associates A061037 with A106617.

Original entry on oeis.org

4, 1, 2, 1, 2, 1, 2, 1, 4, 1, 2, 1, 1, 1, 2, 1, 4, 1, 2, 1, 2, 1, 2, 1, 4, 1, 2, 1, 1, 1, 2, 1, 4, 1, 2, 1, 2, 1, 2, 1, 4, 1, 2, 1, 1, 1, 2, 1, 4, 1, 2, 1, 2, 1, 2, 1, 4, 1, 2, 1, 1, 1, 2, 1, 4, 1, 2, 1, 2, 1, 2, 1, 4, 1, 2, 1, 1, 1, 2, 1, 4, 1, 2, 1, 2, 1, 2, 1, 4, 1, 2, 1, 1, 1, 2, 1, 4, 1, 2, 1, 2

Offset: 0

Jean-François Alcover and Paul Curtz, Sep 09 2014

This sequence may also be defined as the denominators of A061037(n+3)/(n+1), or also as A060819 / A109008.

One can notice that the analog numerators [numerators of (n+4)/gcd(n, 4)^2] are A106617 left-shifted 4 places.

			Fractions begin:
1/4,  5,  3/2,  7, 1/2,  9,  5/2, 11, 3/4, 13,  7/2, 15, 1, 17,  9/2, 19,
5/4, 21, 11/2, 23, 3/2, 25, 13/2, 27, 7/4, 29, 15/2, 31, 2, 33, 17/2, 35,
...
Numerators begin:
1,  5,  3,  7, 1,  9,  5, 11, 3, 13,  7, 15, 1, 17,  9, 19,
5, 21, 11, 23, 3, 25, 13, 27, 7, 29, 15, 31, 2, 33, 17, 35,
...
Periodic part = [4, 1, 2, 1, 2, 1, 2, 1, 4, 1, 2, 1, 1, 1, 2, 1];

Antti Karttunen, Table of n, a(n) for n = 0..65537
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1).

Cf. A060819, A061037, A106617, A109008, A188134, A213268.

[Denominator((n+4)/Gcd(n,4)^2): n in [0..100]]; // G. C. Greubel, Aug 05 2018

a[n_] := (n+4)/GCD[n, 4]^2 // Denominator;  Table[a[n], {n, 0, 100}]
(* or: *)
Table[{1, 2, 1, 2, 1, 2, 1, 4, 1, 2, 1, 1, 1, 2, 1, 4}[[Mod[n, 16, 1]]], {n, 0, 100}]

for(n=0,100, print1(denominator((n+4)/gcd(n,4)^2), ", ")) \\ G. C. Greubel, Aug 05 2018

A247004 = A060819 / A109008.
(n+4) / gcd(n, 4)^2 = A188134(n+4) / 4. - Michael Somos, Sep 12 2014
a(n) = a(n+16) = a(-n), a(2*n + 1) = 1 for all n in Z. - Michael Somos, Sep 13 2014

cp's OEIS Frontend

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

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A283443 a(n) = lcm(n,6) / gcd(n,6).

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A070293 a(n) = lcm(30,n)/gcd(30,n).

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A283444 a(n) = lcm(n,7) / gcd(n,7).

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A247004 Denominator of (n+4)/gcd(n, 4)^2, a 16-periodic sequence that associates A061037 with A106617.

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