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%I #13 Jun 19 2018 12:10:38
%S 1,1,2,4,4,8,12,18,24,30,30,40,48,60,72,84,96,112,128,146,164,184,204,
%T 226,248,272,296,322,336,364,392,422,452,484,516,550,584,620,656,694,
%U 732,772,812,854,896,940,984,1030,1076,1124,1172
%N a(0) = 1; a(n) = a(n-1) + n - gcd(n,a(n-1)).
%H G. C. Greubel, <a href="/A135268/b135268.txt">Table of n, a(n) for n = 0..1000</a>
%F a(n) = c*n*(n-1), where c ~ 0.48....
%e a(8) = 18 + 8 - gcd(8,18) = 18 +8 -2 = 24.
%p a[0]:=1: for n to 50 do a[n]:=a[n-1]+n-gcd(n,a[n-1]) end do: seq(a[n],n=0.. 50); # _Emeric Deutsch_, Feb 28 2008
%t RecurrenceTable[{a[n] == a[n - 1] + n - GCD[n, a[n - 1]], a[0] == 1}, a, {n, 0, 25}] (* _G. C. Greubel_, Oct 08 2016 *)
%t nxt[{n_,a_}]:={n+1,a+n+1-GCD[n+1,a]}; NestList[nxt,{0,1},50][[All,2]] (* _Harvey P. Dale_, Jun 19 2018 *)
%o (PARI) first(n)=my(v=vector(n)); v[1]=1; for(k=2,n,v[k]=v[k-1]+k-gcd(k,v[k-1])); concat(1,v) \\ _Charles R Greathouse IV_, Oct 08 2016
%K easy,nonn
%O 0,3
%A _Ctibor O. Zizka_, Feb 15 2008, Feb 21 2008
%E Corrected and extended by _Emeric Deutsch_, Feb 28 2008
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