[seqfan] Questions concerning A003418 and A002944.

peter.luschny at googlemail.com peter.luschny at googlemail.com
Tue Jun 23 19:30:23 CEST 2009

A003418(n) = lcm({1,2,3,...,n}) 	 	
A002944(n) = lcm({1,2,3,...,n})/n

(1) A003418: seq (denom(sum((-1)^i/i, i = 1..n)), n=0..30);"
(Zerinvary Lajos) looks erroneous. First discrepancy at n=16.
Perhaps the author meant A058312(n).  And PARI?

(2) A003418: "It appears that A020500(n) = A003418(n+1)/a(n)"

Better: "It appears that A014963(n) = A003418(n)/A003418(n-1)"
This is indeed true, as also indicated as the first formula in A014963:
A014963(n) = LCM {1..n}/LCM {1..n-1}.

(3) A002944: BB := n->sum(1/sqrt(k), k=1..n): a := n->floor(denom(BB(n))/n):
(Zerinvary Lajos) is not clear to me. Replacing 'sum' by 'add' certainly
would give wrong values.

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