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LCM of {C(0,0), C(1,0), ..., C(n, floor(n/2))}.
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%I #16 Nov 01 2023 03:18:35

%S 1,1,2,6,6,30,60,420,420,1260,1260,13860,13860,180180,360360,360360,

%T 360360,6126120,6126120,116396280,116396280,116396280,116396280,

%U 2677114440,2677114440,13385572200,13385572200,40156716600,40156716600,1164544781400

%N LCM of {C(0,0), C(1,0), ..., C(n, floor(n/2))}.

%H Robert P. P. McKone, <a href="/A025552/b025552.txt">Table of n, a(n) for n = 0..199</a>

%F Let b(n) = 2 if n = 2^m or n = 2^m + 1 for some m, otherwise 1; then a(n) = lcm({1,2,...,n}) / b(n). - _Peter Luschny_, Jun 26 2009

%p LCM := proc(n) option remember; if n < 2 then 1 else ilcm(n,LCM(n-1)) fi end;

%p a := proc(n) local i; add(i,i=convert(2*iquo(n+2,2),base,2)); `if`(%=1, LCM(n), LCM(n)/2) end: # _Peter Luschny_, Jun 26 2009

%t l[1] = 1; l[n_Integer?NonNegative] := l[n] = LCM[n, l[n - 1]];

%t a[0] = 1; a[n_Integer?NonNegative] := a[n] = Module[{s}, s = Total[IntegerDigits[2*Quotient[n + 2, 2], 2]]; If[s == 1, l[n], l[n]/2]];

%t Table[a[n], {n, 0, 29}] (* _Robert P. P. McKone_, Oct 31 2023 *)

%Y Cf. A003418. - _Peter Luschny_, Jun 26 2009

%K nonn

%O 0,3

%A _Clark Kimberling_

%E Offset corrected by _Peter Luschny_, Jun 26 2009