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
EXAMPLE
lcm(1,1')/gcd(1,1')+lcm(2,2')/gcd(2,2')+lcm(3,3')/gcd(3,3')=0+2/1+3/1=5 ->a(3)=5.
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=1..n), n=1..50);
MATHEMATICA
A003415[n_]:= If[Abs@n < 2, 0, n Total[#2/#1 & @@@FactorInteger[Abs@n]]];
Table[Sum[LCM[k, A003415[k]]/GCD[k, A003415[k]], {k, 1, n}], {n, 1, 50}] (* G. C. Greubel, Dec 29 2017 *)
PROG
(PARI) {A003415(n, f)=sum(i=1, #f=factor(n)~, n/f[1, i]*f[2, i])};
for(n=1, 50, print1(sum(k=1, n, lcm(k, A003415(k))/gcd(k, A003145(k))), ", ")) \\ G. C. Greubel, Dec 29 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Giorgio Balzarotti, May 04 2011
STATUS
approved