cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

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

Views

Author

Colin Barker, Mar 07 2017

Keywords

Links

Crossrefs

Cf. A064680, A130724, A188134, A283443, A283444.
Cf. A109009, A109046.

Programs

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

Formula

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

Views

Author

Colin Barker, Mar 07 2017

Keywords

Comments

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

Links

Crossrefs

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

Programs

  • Mathematica
    Table[LCM[n, 6] / GCD[n, 6], {n,0,63}] (* Indranil Ghosh, Mar 08 2017 *)
  • PARI
    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)))
  • PARI
    {for (n=0, 63, print1((lcm(n, 6) / gcd(n, 6)),", "))}; \\ Indranil Ghosh, Mar 08 2017

Formula

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

Views

Author

Amarnath Murthy, May 10 2002

Keywords

Crossrefs

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

Programs

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

Formula

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

Extensions

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

Views

Author

Colin Barker, Mar 07 2017

Keywords

Comments

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

Links

Crossrefs

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

Programs

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

Formula

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
Showing 1-4 of 4 results.

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