A129091
a(0)=1; a(n) = gcd(a(n-1), n) + lcm(a(n-1), n).
Original entry on oeis.org
1, 2, 4, 13, 53, 266, 800, 5601, 44809, 403282, 2016412, 22180533, 88722135, 1153387756, 8073714294, 40368571473, 645897143569, 10980251440674, 32940754322028, 625874332118533, 12517486642370661, 12517486642370682
Offset: 0
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a[0]:=1: for n from 1 to 25 do a[n]:=gcd(a[n-1],n)+lcm(a[n-1],n) od: seq(a[n],n=0..25); # Emeric Deutsch, Apr 02 2007
A309705
a(n) = lcm(a(n-1), n) - gcd(a(n-1), n) where a(1) = 1.
Original entry on oeis.org
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
For n = 5, since a(4) = 2, a(5) = lcm(5,2) - gcd(5,2) = 10 - 1 = 9.
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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
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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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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
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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))
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