OFFSET
1,2
COMMENTS
Use lcm(1,0)=0 and gcd(1,0)=1.
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..10000
FORMULA
a(n) = Sum_{k=1..n} k*A189036(k).
EXAMPLE
lcm(1,1')/gcd(1,1')*1+lcm(2,2')/gcd(2,2')*2+lcm(3,3')/gcd(3,3')*3=0+2/1*2+3/1*3=13 ->a(3)=13.
MAPLE
der:=n->n*add(op(2, p)/op(1, p), p=ifactors(n)[2]):
seq(add(lcm(der(i), i)/gcd(der(i), i)*i, i=1..n), n=1..50);
MATHEMATICA
A003415[n_]:= If[Abs@n < 2, 0, n Total[#2/#1 & @@@FactorInteger[Abs@n]]];
Table[Sum[k*LCM[k, A003415[k]]/GCD[k, A003415[k]], {k, 1, n}], {n, 1, 50}] (* G. C. Greubel, Dec 29 2017 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Giorgio Balzarotti, May 04 2011
STATUS
approved