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

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

Author

Colin Barker, Mar 07 2017

Keywords

• nonn
• easy

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

• 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).

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