A309705 a(n) = lcm(a(n-1), n) - gcd(a(n-1), n) where a(1) = 1.
1, 1, 2, 2, 9, 15, 104, 96, 285, 565, 6214, 37282, 484665, 6785309, 101779634, 814237070, 13842030189, 83052181131, 1577991441488, 7889957207436, 55229700452049, 1215053409945077, 27946228428736770, 111784913714947074, 2794622842873676849, 72660193914715598073
Offset: 1
Keywords
Examples
For n = 5, since a(4) = 2, a(5) = lcm(5,2) - gcd(5,2) = 10 - 1 = 9.
Links
- Alois P. Heinz, Table of n, a(n) for n = 1..500
Programs
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Maple
a:= proc(n) option remember; `if`(n=1, 1, ilcm(a(n-1), n)-igcd(a(n-1), n)) end: seq(a(n), n=1..29); # Alois P. Heinz, Sep 17 2019 -
Mathematica
a[1] = 1; a[n_] := a[n] = LCM[a[n - 1], n] - GCD[a[n - 1], n]; Array[a, 26] (* Amiram Eldar, Sep 17 2019 *) nxt[{n_,a_}]:={n+1,LCM[a,n+1]-GCD[a,n+1]}; NestList[nxt,{1,1},30][[All,2]] (* Harvey P. Dale, Apr 05 2020 *)
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PARI
seq(n)={my(v=vector(n)); v[1]=1; for(n=2, #v, v[n] = lcm(v[n-1], n) - gcd(v[n-1], n)); v} \\ Andrew Howroyd, Aug 28 2019 -
Python
def lcmMinusGcd(n): retlist = [1] for i in range(1, n): g = gcd(retlist[i-1], i+1) retlist.append( floor(retlist[i-1]*(i+1) / g) - g) return ', '.join(map(str,retlist))
Formula
a(n) = lcm(a(n-1), n) - gcd(a(n-1), n) for n > 1.
Comments