A190120 a(n) = Sum_{k=1..n} lcm(k,k')/gcd(k,k'), where n' is arithmetic derivative of n.

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

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) {A003145(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, A003145(k))/gcd(k, A003145(k))), ", ")) \\ G. C. Greubel, Dec 29 2017

Crossrefs

Cf. A003415, A190118, A190119.

Sequence in context: A051217 A275522 A110975 * A069789 A332683 A086334

Adjacent sequences: A190117 A190118 A190119 * A190121 A190122 A190123

Keyword

nonn

Author

Giorgio Balzarotti, May 04 2011

Status

approved