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A190120
a(n) = Sum_{k=1..n} lcm(k,k')/gcd(k,k'), where n' is arithmetic derivative of n.
2
0, 2, 5, 6, 11, 41, 48, 54, 60, 130, 141, 153, 166, 292, 412, 414, 431, 473, 492, 522, 732, 1018, 1041, 1107, 1117, 1507, 1508, 1564, 1593, 2523, 2554, 2564, 3026, 3672, 4092, 4107, 4144, 4942, 5566, 5736, 5777, 7499, 7542, 7674, 7869, 9019, 9066, 9087, 9101, 9191
OFFSET
1,2
COMMENTS
Use lcm(1,0)=0 and gcd(1,0)=1.
LINKS
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